equality versus isomorphism part. For instance the discussion of natural isomorphism was confusing as it made it seem as if whether an isomorphism was natural...

familiar with any standard reference to the isomorphism theorems that calls them "Noether's Isomorphism Theorems". Even if the attribution is accurate...

The comment(s) below were originally left at Talk:Quasi-isomorphism/CommentsTalk:Quasi-isomorphism/Comments, and are posted here for posterity. Following...

(UTC) The first paragraph states that a musical isomorphism can also be called canonical isomorphism. This is in disagreement with http://en.wikipedia...

the article? Order isomorphisms between posets are explicitly mentioned in the section Isomorphism#Relation-preserving_isomorphism, for example. JBL (talk)...

Channel-state duality says "This map is also called Choi–Jamiołkowski isomorphism" and this article says they are synonymous. Are these the same thing...

"order isomorphism of partially ordered groups" or "order isomorphism of po-groups"). The cited source refers to order isomorphisms as "o-isomorphisms" for...

and Fein (1999) say these are not distinct types of isomorphism, but rather ways for isomorphism to merge. Robertekraut (talk) 19:52, 2 October 2015 (UTC)...

this, consider the isomorphism class of the null set in Part, it contains only the null set. On the other hand, each isomorphism class of Set* contains...

available software for testing graph isomorphism. Here is just a couple of reasons for that: Testing graph isomorphism is of great practical importance;...

"isomorphism theorems" would seem appropriate as the title. Comments? Michael Hardy 01:12 Mar 21, 2003 (UTC) It would make sense to use Isomorphism theorems...

Specifically, graph isomorphism is the special case of subgraph isomorphism in which the subgraph to be checked for being an isomorph has the same number...

confusion between this and NP-intermediate, which implies that Group Isomorphism is not only decidable, but no worse than NP-hard. 130.126.255.15 (talk)...

"isomorph (Dynamic Energy Budget theory)". Even in the context of biology, the usual definition of isomorph is "an organism that exhibits isomorphism"...

Andreas Blass's "Seven Trees in One" a relevant example of an isomorphism? There is an isomorphism between the set of figures binary trees and the seven-fold...

isomorphism. - 80.143.112.207 11:57, 20 January 2007 (UTC) Nice point, but a homomorphism preserves structure in a possibly-lossy way. An isomorphism...

Is there a standard symbol for this relation? Like isomorphism-subscript-c? —Preceding unsigned comment added by 128.100.216.124 (talk) 20:00, 27 April...

I've completed it. If anyone knows of another algorithm for subgraph isomorphism, please don't hesitate to mention it (especially if it's simpler, and...

are the bullet "mesh isomorphism" in the introduction, and section 6, "Mesh Isomorphism". The graphs to be tested for isomorphism come equipped with an...

made to this discussion. This review is transcluded from Talk:Cantor's isomorphism theorem/GA1. The edit link for this section can be used to add comments...

10:33, 28 April 2010 (UTC) The article doesn't specify what kind of isomorphism it is (groups/rings, with respect to what products). — Preceding unsigned...

The problem is only minimally different from subgraph isomorphism. Replacing implication by equivalence would change the latter into the former. Moreover...

fellow Wikipedians, I have just modified one external link on Graph isomorphism problem. Please take a moment to review my edit. If you have any questions...

Please, think there also about isomorphism classes of graphs. Канеюку (talk) 16:21, 11 November 2011 (UTC) The article is a bit vague about what it means...

Kolmogorov–Arnold representation theorem? I don't think we can see it in terms of isomorphism. What about the representation theorems in logic that show semantic equivalence...

Cohesive Isomorphism In some situations isomorphism in a cohesive way must be chosen. This is often achieved by choosing a canonical isomorphism. But in...

"the Myhill isomorphism theorem", or to "a complexity-theoretic analogue". Perhaps it can be phrased better. Maybe "(...) Myhill isomorphism theorem. They...

March 2006 (UTC) An isomorphism between a vector space and its dual V* is perhaps the commonest example of a non-natural isomorphism. Is there a sense in...

18 July 2016 (UTC) I've added the definition of isomorphism; not every homomorphism is an isomorphism. Andrewbt (talk) 05:45, 31 December 2017 (UTC) Another...

groups. Hence, there is an isomorphism between the category of groups and the category of discrete groups..." Is the isomorphism to the category of discrete...

similar to "isomorphism theorem" versus "isomorphism theorems". The latter sounds more natural due to there being a few of them. Isomorphism theorem begins...

generalization of "isomorphism" but I can't think of a ten-word explanation. Besides being a not-very-deep generalization of "isomorphism", the homomorphism...

cohomology groups. The Thom isomorphism, on the other hand, can be interpreted as a generalization of the suspension isomorphism. For a space B {\displaystyle...

meaningful definition (e.g. natural isomorphism, isomorphism which commutes with this list of stuff-which-isomorphisms-might-commute-with but not necessarily...

explanation of the difference between isomorphisms and equivalences? The article on isomorphism says the following: Isomorphism of categories is a very strong...

and any monotone increasing function on the reals will induce an order isomorphism of the rationals to their image. Are there any other interesting known...

needed here. See the general definition in the the lead of Isomorphism, which defines an isomorphism as a "bijective homomorphism". Definitions in category...

PGL(3,2). Revolver If anyone is familiar with the actual isomorphism (or AN actual isomorphism) between PSL(2,7) and SL(3,2), this would be great. I did...

Ceasars Salad (talk) 21:07, 23 October 2016 (UTC) If the isomorphism is "crystallography" why isomorphism is "geology"? --Mimozul (talk) 06:37, 27 October 2018...

the isomorphism is unique then. You can count this as an extension of Mostowski lemma to nonextensional relations which does give an isomorphism. — EJ...

natural isomorphism should be...' If it was like that already, I apologize. I can't remember. -- mat_x 21:17, 28 Jul 2004 (UTC) Every natural isomorphism will...

C*-structure: isomorphisms on the level of algebras gives homeomorphisms on spaces. The statement of Banach-Stone is stronger than that: isomorphism of Banach...

article. From the text, "However, Morita equivalence is not equivalent to isomorphism. It is possible, but extremely difficult, to distinguish between non-isomorphic...

B is the same thing as an isomorphism from A to an elementary substructure of B. Rather I think it should be "an isomorphism from A to a substructure of...

⊗ o p ) {\displaystyle ({\mathcal {C}},\otimes ^{op})} ? A "natural isomorphism" would mean between two functors between the same categories, so it seems...

(unless the map is an isomorphism). The second version is fine. The above map does not satisfy the hypotheses if it is not an isomorphism. The first version...

The canonical morphism $C_{X/Y} \to N_{X/Y}$ is only an isomorphism when the immersion is regular. ~2026-90258-0 (talk) 22:30, 9 February...

November 2012 (UTC) Professor Babai will soon be presenting a new graph isomorphism algorithm, as reported in multiple locations, so this page is likely...

relations induced by Polish group actions Equivalence relations reducible to isomorphism on countable structures Turbulent actions Louveau-Velickovic relations...

be confused on the notion of isometric isomorphism. The statement is not that the identity map is an isomorphism of one space to the other. They are different...

item asserts "Varieties were often considered only up to birational isomorphism". This is wp:OR. On the other hand, "singularity theory" is an active...

complexity of the isomorphism and automorphism problems for finite rings with unity. We show that both integer factorization and graph isomorphism reduce to the...

double-dual isomorphism), which is a very useful fact, but not the simplest description of an element of V. (2) The claim that there is no isomorphism between...

use the standard categorial definition for "isomorphism" doesn't work here because any such isomorphism would be a bijection between Z n {\displaystyle...

coprime *if and only if* we have the *group* isomorphism. If this is also true for the ring isomorphism then I suggest it be added to the article. Similarly...

A+B} , and a function which is both an injection and a surjection is an isomorphism, but it is not true that (Injections, Surjections) is a factorization...

There's a slight divergence of the definition of isomorphism between this article and group isomorphism. That article defines a g. isom. as "a bijective...

$f^*:H_n(S^n;\Zt)\to H_n(S^n,\Zt)$ is an isomorphism. Thus $$f^*:H_{n-1}(A;\Zt)\to H_{n-1}(A;\Zt)$$ is an isomorphism. By the commutativity of the diagram...

(Dr. Ranajit Das)) , provides a topic on Mitscherlich's law of crystal isomorphism, and one of its application, in a stoichiometry chapter (Rajarshi Rit...

sets, is a set E ⊂ {\displaystyle \subset } ω×ω such that there is an isomorphism between (ω,E) and (X, ∈ {\displaystyle \in } ) where X is the transitive...

this article, even though each is a Hodge isomorphism on its own space. There are two "quasi-Hodge isomorphisms"  ⋆ : ⋀V → ⋀V∗  and  ⋆ : ⋀V∗ → ⋀V , which...

The article states: This hard Lefschetz isomorphism induces canonical isomorphisms R f ∗ ( Q ) → ≅ ⨁ i = − d d R d + i f ∗ ( Q ) [ − d − i ] . {\displaystyle...

isomorphism, rather than depend on the Clifford algebra classification, I have inserted the keys to a direct isomorphism at coquaternion#Isomorphism with...

p}(\mathbb {R} )} These isomorphisms are not mentioned here for unknown reasons. Their proofs are precisely the same, as for the isomorphism C ℓ n , 0 ⊗ H ≅ C...

general reader of what the C-H isomorphism is really about. I had started writing an article about the C-H isomorphism when this article was put up. I...

one. So such an isomorphism cannot respect the topological structure of either Lie group. This can only be an abstract group isomorphism. I seriously doubt...

automorphism group ..". So, what is this group? (Or, pedantically, what is its isomorphism class?) Is it PSL2(13)? Maproom (talk) 15:25, 21 November 2013 (UTC)...

etale by this definition, and there are proper class many different isomorphism class of these uninteresting etale covers. Milne requires the maps in...

seems to imply that the tautological one-form establishes a canonical isomorphism between T Q {\displaystyle TQ} and T ∗ Q {\displaystyle T^{*}Q} that...

wondering about the de Rham isomorphism. In Bott&Tu there is a proof of this for finite good covers. Does this isomorphism still exist otherwise? I think...

constitute a dual pair, this isomorphism carries over to the entitative graphs. (A better, but less known, term than "isomorphism" is Tarski's "equipollence"...

* There is a canonical Künneth isomorphism H*(X) ⊗ H*(Y) → H*(X × Y) ≅ K What is the K? Any Weil cohomology theory factors uniquely through the category...

Planar graph isomorphism -- Samir Datta, Nutan Limaye, Prajakta Nimbhorkar, Thomas Thierauf, and Fabian Wagner. Planar Graph Isomorphism is in Log-Space...

to be an isomorphism" The above suggests that principal polarizations may not be isomorphisms. Principal polarizations are always isomorphisms. The theta-divisor...

spaces discussion, the isomorphism has been clarified and even shown to apply to L^infinity. I still think that the isomorphism should be described in...

order-preserving isomorphism from its ordered additive group to its ordered multiplicative group of positive elements also admits such an isomorphism with the...

_{r}(H)=\{z_{s}|Hs=H,s\in S^{1}\}} the right one. Then, only this natural isomorphism φ : Γ r ( H ) → Γ l ( H ) {\displaystyle \varphi :\Gamma _{r}(H)\rightarrow...

as "bicategory" (to my understanding). A bicatgeory is a weak 2-category, where associativity holds only up to coherent isomorphism, as stated here....

three)? Source [2] talks about a Baumgartner problem: BAUMGARTNER’S ISOMORPHISM PROBLEM FOR ℵ2-DENSE SUBORDERS OF R. Accordingly, I deleted the statement...

book I've looked in calls it either "Correspondence theorem" or 4th isomorphism... 86.127.138.67 (talk) 02:49, 17 April 2015 (UTC) Since nobody had anything...

on graph theory and also consistent with the notation at Isomorphism and Graph isomorphism. McKay (talk) 07:42, 29 August 2024 (UTC) See Graph homomorphism...

There should also be a page on Cartier operator related to the Cartier isomorphism on de Rham cohomology in char p, as in the Deligne Illusie proof of Hodge...

(talk) 08:25, 27 November 2010 (UTC) Thanks; in fact there are three isomorphism classes over the real numbers. Mark M (talk) 09:50, 16 December 2013...

very next sentence uses singular. Is there only one G2 group (up to isomorphism) or are there many? 67.190.17.110 13:55, 15 February 2007 (UTC) BL Well...

inaccuracies on this page. Katzmik 12:59, 21 August 2007 (UTC) In the Nielsen Isomorphism Theorem section, someone is apparently disputing the accuracy of the...

06:04, 28 October 2007 (UTC) I know some mathematicians that call the isomorphism between a vector space and its dual (given by an inner product), Poincare...

if appropriate, a page for Isomorph_(crystallography) and an Isomorph disambiguation page, and improve the Isomorphism (disambiguation) page. Perhaps...

and then proceed to point out the isomorphism with S3, defined in terms of permutations? As it stands, the isomorphism is tacitly assumed, and the geometric...

corrected, the statement that the cohomology group H^1(X,G) parametrizes isomorphism classes of torsors is erroneous (take G=1 and X=point). A torsor can...

In terms of isomorphism, maybe? - Altenmann >talk 23:11, 7 November 2023 (UTC) It appears to mean that there are at most two isomorphism classes of splits...

{\displaystyle {\mathcal {O}}_{X}\rightarrow f_{*}{\mathcal {O}}_{Y}} is an isomorphism (of sheaves). This implies that X {\displaystyle X} is normal....

{\hat {\mathbb {Z} }}} . Furthermore, this is an isomorphism of abstract groups, but not an isomorphism of topological groups. 93.132.116.137 (talk) 20:13...

starts as follows: An isomorphism is a bijective homomorphism. Two objects are said to be isomorphic if there is an isomorphism between them. Isomorphic...

word ‘isomorphism’ applies when two complex structures can be mapped onto each other,... There are ten different meanings given for isomorphism, this...

Milez (talk) 19:41, 31 October 2013 (UTC) We should separate out the isomorphism T ≅ R ⊕ ( Q / Z ) ≅ C × {\displaystyle \mathbb {T} \cong \mathbb {R}...

a (not necessarily invertible) morphism, but the other is a natural isomorphism. Shouldn't the latter be a (not necessarily invertible) natural transformation...

complete family of deformations where the kodaira-spencer map is an isomorphism Add Bogomolev-Tian-Todorov theorem that the Kodaira-Spencer map of a...

defines a graph invariant as a class of graphs that is closed under isomorphism. A graph invariant is defined as a map taking graphs as arguments which...

}}\cdot {\vec {v}})} is trace zero and Hermitian then we can use the isomorphism between the real vector space of Hermitian trace zero 2x2 complex matrices...

contribs) 00:10, 6 December 2021 (UTC) proof unfinished: In order to prove isomorphism, you also need to show join and meet are preserved, not just bijection...

H^{1}(X,G)} classifies G-torsors (principal bundles) on X. Easy example: isomorphism classes of (holomorphic) C ∗ {\displaystyle \mathbb {C} ^{*}} -principal...

Hey, up to isomorphism there is only one real n-dimensional vector space. Up to isomorphism there is only one real-dimensional Slawomir Bialy. Of course...

article currently reads, "In mathematics, a symplectomorphism is an isomorphism in the category of symplectic manifolds." The category of symplectic...

snake lemma can be used to prove the 3rd isomorphism theorem (by the numbering in the wikipedia article 'Isomorphism Theorems') would be a nice thing to include...

How do you know that these are the only isomorphism classes? — Preceding unsigned comment added by 134.60.66.123 (talk) 2008-09-01T12:32:24Z This is Satz...

I've added a sentence to the lead saying Up to isomorphism, there is only one nontrivial standard Borel space. I don't expect it to stay that way, but...

Spakoj 12:34, 2 May 2006 (UTC) Over the rational numbers, there is an isomorphism from the additive formal group law to the multiplicative one, given by...

In general we have isomorphism => bimorphism (mono+epi) => bijective morphism. The category Top is not balanced because the converse of the first arrow...

be at least a link with "the adjoint to i'. The assertion that "this isomorphism is not the same and the composition of the inclusion i with its adjoint...

November 2005 (UTC) No, you've forgotten the condition on cones, and isomorphism does follows from initiality. --- Charles Stewart 16:20, 2 November 2005...

as D* for some D. An equivalence allows us to say that and then the isomorphism gives the desired A** isomorphic to A. To see that I* is the dualising...

inclusion of the subcategory of all N such that N -> Hom( m , N ) is an isomorphism. (These are true for any Gabriel localization.) — Preceding unsigned...

2015 (UTC) In what way can we speak of the algebraic closure? The K-isomorphism is non-canonical in general. --84.165.192.126 09:55, 30 August 2005 (UTC)...

should be. There is also the tacit understanding that you work with isomorphism classes rather than with the original objects; c. f. your "Bemerkung"...

here. And the invertible vector bundle map from TM to V? That's just an isomorphism of vector bundles? So this is all a way of saying that TM can be reduced...

15:52, 3 April 2025 (UTC) If there are secondary sources for that, this isomorphism(?) must be explicited in a section of Field with one element. When done...

...

algebra homomorphism from the space ..." More specifically, isn't it an isomorphism, and if so should we say this instead? 128.243.253.102 (talk) 15:24,...

IC_X --> D_X which induces a dual pairing, but it is almost never an isomorphism. It's not immediately clear how to fix the original author's intended...

has an inverse and thus only n = 0 is an isomorphism. It is difficult to get closer to the notion of isomorphism while remaining strictly weaker than with...

consideration. The real numbers are defined by their axiomatisation, up to isomorphism, and so are the topological spaces. However, "axioms" of countability...

their degree, there is some K-isomorphism from F1 to F2, for each pair of splitting fields F1,F2 ≤ B. This isomorphism is inner by N-S, so F1 and F2 are...

theorem states that birational equivalence of varieties is identical to isomorphism of their function fields as extensions of the base field." But no mention...

single entity. If this object is a class of transformations (such as "isomorphism" or "permutation"), it implies the equivalence of objects one of which...

a factorization system. Instead in my proof I need subobjects (i.e. isomorphism classes of monomorphisms) to show that every morphism factors through...

--IkamusumeFan (talk) 00:48, 25 June 2015 (UTC) Any monic split epimorphism is an isomorphism. The proof is below. f ∘ ( g ∘ f ) = ( f ∘ g ) ∘ f = 1 Y ∘ f = f = f...

first isomorphism, no, it really depends on a category. The first isomorphism theorem of Lie group is not the same thing as the first isomorphism theorem...

article is about two disjoint classes of functions, that have some kind of isomorphism a the top level but are otherwise separate topics, and that it should...

section entitled "word problem". Surely this section is discussing the isomorphism problem?!? —Preceding unsigned comment added by 130.209.6.40 (talk) 12:51...

coefficients) and conic quaternions. Sorry for the mixup. That's the correct isomorphism which I wanted to write about at the beginning, but I mixed it all up...

one unique up to isomorphism". But this is a universal issue in mathematics: when is equality "equality" and when is it just "isomorphism", and do we only...

2007 (UTC) Injectivity of a k-algebra homomorphism isn't enough for an isomorphism. Let k be a field and K an extension field such that k ≠ K {\displaystyle...

called a monomorphism. An isomorphism of A with B is defined to be a one-one morphism from A onto B; an automorphism is an isomorphism of an algebra with itself...

mathematically proven that GNNs are a weak form of the Weisfeiler–Lehman graph isomorphism test, so any GNN model is at most as powerful as this test. On the basis...

...

non-commutative groups G, since in that case the appropriate dual object G^ of isomorphism classes of representations cannot only contain one-dimensional representations...

this seems like a description which does not merit a new name beyond "isomorphism". A "verbal walk" starting from these misapprehensions and correcting...

this relative cohomology class? Thanks, Jack You can get it from Thom Isomorphism H r ( F , F ∖ F 0 ; Z ) = H 0 ( X , Z ) {\displaystyle H^{r}(F,F\setminus...

ℤ⊕ℤ is not sufficient to show Ker∂/Im∂ ≅ ℤ - consider ℤ/2ℤ, 2ℤ ≅ ℤ. An isomorphism must be constructed carrying the boundary image to ℤ⊕ℤ⊕0 ≤ ℤ⊕ℤ⊕ℤ. Finishing...

depends on the supposed possibility of assigning an order type to every isomorphism type of well-orderings, combined with the observation that the order...

rather than an isomorphism class. On the other hand category theorists seem to have no qualms about defining objects only up to isomorphism, so if Wikipedia...

it might benefit to mention (I believe it's called) the Conjugation Isomorphism Theorem? It basically says that if two numbers a and b algebraic over...

has a bijection to two piecewise isomorphic sections having a unique isomorphism. Can anyone clarify this? — Preceding unsigned comment added by...

being isomorphic to one is not important, because there is a specific isomorphism between them. This language doesn't really generalize anything, it just...

Matthews 13:05, 29 September 2005 (UTC) Right, got it. Thanks! Is the isomorphism easy to write down? best wishes Robinh 14:35, 29 September 2005 (UTC)...

2014 (UTC)' I just realised that the alleged “simple subgroups of 13 isomorphism types” has absolutely no indication of how they obtained that information...

35.181 (talk) 21:39, 26 May 2008 (UTC) I updated the section on the isomorphism of Hom and Der to be more precise, but the universal property of d:S...

articles. 67.198.37.16 (talk) 18:56, 3 May 2025 (UTC) Citation needed on isomorphism of the filtered algebra and its associated graded algebra. Here is an...

M_{n}(\mathbb {C} )} -valued—continuous functions over X. Also, it is known that isomorphism of vector bundles translates to Murray-von Neumann equivalence of the...

supposed violation of physical laws disappears" This page is defining "isomorphism" read pages 80 - 86 of Bertalanffy: [summarized] multiple disciplines...

completion is an isomorphism if and only if the intersection of the powers of I consists only of zero element of the ring." Should "isomorphism" be "injection"...

formally represented by graphs, the concep of analog is related to a graph isomorphism. Analogical models are used in a method of representing a ‘target system’...

division, and would also make sense in type theory where we have the isomorphism between X and (forall T. (X -> T) -> T) by parametricity. Writing the...

as modular functions extending to the compactification Page 16, show isomorphism of semidirect product as a matrix group Then give the induced action...

the 2-by-2 identity matrix, which one requires to be an isomorphism. Then using this isomorphism, one can construct a method of adding morphisms, which...

isometry is unclear. Try something like "An isometry of forms is an isomorphism of vector spaces which is also metric. Maybe for the references: Artin...

Thus, when talking of "isomorphism" one always need to precise which kind of isomorphisms: isomorphisms of affine spaces, isomorphism of variety, birational...

Schrodinger equation, so in a sense offers no new predictions. It's a kind of isomorphism to conventional QM, only with a deterministic, hidden variable interpretation...

{\displaystyle \mathrm {PGL} } , but I do not know if it is an exceptional isomorphism. At the top of the article is a useful-looking diagram showing homomorphisms...

axes'. What x,y,z axes?? Presumably this is implicitly(!) under the isomorphism between SU(2) and the double cover of SO(3)? This seems like an incredibly...

homomorphism (operation preserving map) and "equivalent representaion" for isomorphism. As this is not the language Wikipedia uses, and would only clutter a...

IC_X --> D_X which induces a dual pairing, but it is almost never an isomorphism. It's not immediately clear how to fix the original author's intended...

The content of the Isomorphism classIsomorphism class page was merged into Isomorphism#Isomorphism class on 29 October 2024. For the contribution history...

the tensor product of finite-dimensional free modules that we have the isomorphism M ⊗R N ≈ HomR(M, N∗), where M is a right R-module and N is a left R-module...

may suffice to say that Lusztig gave in non-modular cases an explicit isomorphism between generic Hecke algebra and the group algebra of W. Note that this...

foundations of mathematics beyond set theory, in particular "uniqueness up to isomorphism" advances in automation of theorem proving (Martin-Löf Type Theory) connecting...

"reciprocal" Böttcher Isomorphism (by reciprocal, I just mean moving the point at infinity to one at zero through a conformal isomorphism). Furthermore, some...

—David Eppstein (talk) 08:11, 4 March 2024 (UTC) Is it different from isomorphism? —Tamfang (talk) 06:53, 30 March 2024 (UTC) Yes. It is a stronger condition...

product is unique, when it should be explicit that it's unique up to isomorphism. Also, I think a negative example should be provided; for example, in...

May 2008 (UTC) I've never seen ⇒ {\displaystyle \Rightarrow } for an isomorphism. You mention algebra papers, and while it's true that I'm not an algebraist...

Herpesklaus (talk) 19:11, 16 April 2026 (UTC) complex conjugation is an isomorphism of fields. C \subseteq C is the trivial extension. there is no confusion...

importance scale. Rocks and minerals Low‑importance Earth sciences portal Isomorphism (crystallography) is part of WikiProject Rocks and minerals, an attempt...

14:16, 6 August 2009 (UTC) It is mentioned at Binary icosahedral group#Isomorphisms. It could fruitfully be mentioned in the lead as well. JackSchmidt (talk)...

14:08, 13 August 2010 (UTC)Chuck Weibel Given that the norm residue isomorphism theorem was announced to have a complete proof last year, this page could...

initial text, and in describing metric tensors explain the cannonical isomorphism. I believe that the other article already does that. -- Shmuel (Seymour...

give definitions. That R is the unique complete ordered field up to isomorphism is a property of R, after it has been defined. Alternatively, it is a...

Infinite dimension should be covered, too. See Banach space#Linear operators, isomorphisms, [1] etc. Boris Tsirelson (talk) 06:00, 8 December 2016 (UTC)...

August 2010 (UTC) I don't see any utility in listing the numbers of isomorphism classes of groups of small order, especially since the groups themselves...

(UTC) There might be some expansion required, but TM=MxRn up to bundle isomorphism is a consequence of the definition of trivial bundle, so is mentioned...

2020 (UTC) Yes, the second definition has morphisms similar to an order isomorphism or a Galois connection, but based on a homogeneous relation. It is listed...

same as fixing an isomorphism with Rn, hence produces a special isomorphism V→V*, because Rn does possess a preferred isomorphism with its dual, that...

functions only up to several canonicl isomorphisms (isomorphism between polynomials and polynomial functions and isomorphism between ⁠ C {\displaystyle \mathbb...

contains a dodecahedral subgraph or not, I finally installed a subgraph isomorphism solver called Glasgow https://github.com/ciaranm/glasgow-subgraph-solver...

for instance an atomless countable Boolean algebra (it is unique up to isomorphism). Its Stone space is the Cantor set (up to homeomorphism). Which way...

\operatorname {Hom} _{\mathbb {Z} }(\mathbb {Q} ,\mathbb {Z} )} is an isomorphism.89.13.163.119 (talk) 20:32, 30 December 2014 (UTC) The concept of pairing...

every finite dimensional Lie algebra g over F there is a unique (up to isomorphism) simply connected Lie group G with g as Lie algebra." is this really...

integral domain) must be a prime power. Conversly, there exists (up to isomorphism) exactly one finite filed of order a prime power. — Preceding unsigned...

A {\displaystyle \operatorname {ran} A} ⁠ to be the inverse of this isomorphism, and on ( ran ⁡ A ) ⊥ {\displaystyle \left(\operatorname {ran} A\right)^{\perp...

associated with a graph that stays the same (= is invariant) under the graph isomorphism. For instance, the sum of the elementes of the first row of the adjacency...

Perhaps there is a representation theorem that can make this okay if isomorphism is swapped for equality. I am not very familiar with this stuff yet,...

example, the category of all R-S bimodules is abelian, and the standard isomorphism theorems are valid for bimodules." Consider Z as the obvious Z-Z bimodule...

--- and if X {\displaystyle X} is simply connected ("1-connected") the isomorphisms are natural; but neither of these results need hold outside the specific...

LaTeX'd equation is: i\overbar{W} = W^{\perp \perp} It is an injective isomorphism, so should this be i( \overbar{W} ), maybe even with an isomorphic equality...

isomorphism Φ B : V → K n {\displaystyle \Phi _{\mathcal {B}}:V\rightarrow K^{n}} . The space of bases is equivalently the space of such isomorphisms...

10:07, 15 February 2010 (UTC) Could someone also prove uniqueness up to isomorphism? I think that would be a nice addition to the article. Thanks, Maks....

5 using T-spectra Discuss A^1 localization Give diagram showing the isomorphism P^1/A^1 \cong T pg 417 gives the definition, note the negative smash...

distinction between an isomorphism of fields and an isomorphism of ordered fields doesn't make sense for real closed fields: an isomorphism maps squares into...

(V\otimes V^{*},K)} giving us an isomorphism between the linear endomorphisms and the type-(1,1) tensors. I'll ignore the isomorphism from ( V ⊗ V ∗ ) ∗ {\displaystyle...

non-crystaline structure. --PedroDaGr8 22:11, 21 March 2007 (UTC) The isomorph link goes to a page about organisms, that probable should be changed. Dracomaster4...

need not be the only involutory anti-isomorphism but if a regular semigroup has an involutory anti-isomorphism then the inverses are unique and so it...

examples? See also the end of the next subsection "Transport of structures; isomorphism". I can write the definition, but should I? Probably not. It is technical...

one takes sets of structures in an arbitrary signature, closed under isomorphism, whose description is recognizable in the given class. It is in this...

other problems that might have one are integer factorization and graph isomorphism, but I know no result regarding whether either of these problems is in...

that the notation (pγlπ) determines the configuration up to incidence isomorphism. But in fact there exists at least one (pγlπ) configuraation that is...

definitions section starts by talking about monomorphisms and their isomorphism classes, but never quite explains why those should be thought of as "an...

...

circumvent the problem, one usually chooses some representative, for each isomorphism class. One possibility is using Scott's trick, as explained in the page...

assumption that graph isomorphism is not in P, a statement is yet undecided. Given a deterministic polynomial algorithm for graph isomorphism, it would be feasible...

would need a factorization system to define things like kernels, so the isomorphism theorems are perhaps not completely general... I don't know of a reference...

V\otimes V^{*}} — Quondum 16:01, 8 August 2013 (UTC) Naturally, there's an isomorphism between tensor products of different vector spaces. But, as far as the...

I think the "de Rham curves" category tag is misplaced… Math MisterY (talk) 16:52, 31 January 2022 (UTC)...

Mead, Andrew (1988). "Some Implications of the Pitch Class-Order Number Isomorphism Inherent in the Twelve-Tone System- Part One". Perspectives of New Music...

...

a vector space up to isomorphism. In the notation Gr(k, n), I do not specify a vector space, I only specify it up to isomorphism. In both notations, the...

linear operator L: T -> X with C = L o B The tensor product is up to isomorphism uniquely specified by this requirement. Using a rather involved construction...

...

definition of three operations on the simplex and a description of a few isomorphisms, but perhaps their significance to statistics is greater than I can tell...

sentence seemed to confuse equality with "can be interchanged by a field isomorphism," or something.) I have removed the offending sentence. --JBL (talk)...

parabolic subgroups perhaps the isomorphism is also suspect (though in that case we have "reliable sources" claiming the isomorphism ! ) — Rgdboer (talk) 01:19...

isomorphic to a graph that can be obtained [...] Isomorphic as in Graph isomorphism? --Abdull (talk) 12:11, 28 July 2008 (UTC) Yes. I replaced the link to...

Zundark, isn't my definition equivalent with yours? My f is an order-isomorphism from Q to Q\[0,2), which is a subset of Q\[0,1]. No!? Btw., I agree with...

edits, originally speaking of an "isometry" that was then replaced by "isomorphism", with the "at most one" phrase added later. I've gone ahead and fixed...

an isomorphism, then we can just define the inverse as being the inverse to this map, and that is coordinate-free. To show the map is an isomorphism, since...

x^-1]/k[x], and the canonical embedding of k[x,x^-1] in k(x) is not an isomorphism. In other words, this family of elements does not span k(x) as a k-vector...

singular complex (M is triangulable), we obtain the following natural isomorphism I {\displaystyle I} . I : H D R ∗ ( M ) ≃ H ∗ ( K ; R ) {\displaystyle...

...

isn't. (church,unchurch) is not an isomorphism between the naturals and "Church Integer", but it is an isomorphism between the naturals and "forall a...

citation: "... there is a unique isomorphism of ordered sets between them." Halmos and Hamilton don't use the term "isomorphism". Morash lists it in the index...

is the ideal sheaf I V / W {\displaystyle I_{V/W}} . Since we have an isomorphism π ∗ : A d ( V ) → A d + r ( q ∗ N X / Y ) {\displaystyle \pi ^{*}:A_{d}(V)\to...

repeat to get a second derivative d2f : U → Lin(X; Lin(X; Y)). Up to isomorphism, Lin(X; Lin(X; Y)) is the same as Lin(X × X; Y). In other words, at each...

It's not very encyclopedic, I know, but an even simple example is that the group of integers under addition is isomorphic to the group of all even integers...

g\in G} so the action on V G {\displaystyle V^{G}} is trivial (as an isomorphism). --Xtquique (talk) 19:20, 14 August 2014 (UTC)xtquique Elementary examples...

wrong. Flipping the direction of the inner circle alone is not a valid isomorphism of the split-octonions.Utesfan100 (talk) 04:27, 18 January 2013 (UTC)...

not relevant to the field of computer science but more philosophy, "isomorphisms" etc rather than "similarities" .. this article is by a pretend intellectual...

this out. Username6330 (talk) 08:02, 29 September 2017 (UTC) Mention isomorphism between P ( 2 , 3 ) {\displaystyle \mathbb {P} (2,3)} and the moduli...

anti-isomorphism relation is the same as the isomorphism equivalence relation. If you're referring to the specific map not being an isomorphism -- I don't...

observation that there is a natural transformation (in fact, a natural isomorphism) from the functor F to the functor G, where natural has exactly the meaning...

isomorphism. may not satisfy them; what is an automorphism of V? What is the relationship between V and n and F? What does it mean for an isomorphism...

What does this mean? It's easy to see that G r = G ( K ) / G ( O ) {\displaystyle Gr=G(K)/G(O)} is grassmannian. It seems as if "grassmannian" is being...

...

a vector space isomorphic to the Lie algebra. Of course due to this isomorphism one can abuse language and call R3 also the Lie algebra. But I think...

section, I’m pretty sure the source of the natural isomorphism φ should be Hom(-, L), as it is an isomorphism between contravariant functors. For the same reason...

lower down the page Property 4 states "The Fourier transform is a linear isomorphism \mathcal{S} \to \mathcal{S}." Implying the FT is always invertible in...

as defined here, doesn't have a natural topology until one selects an isomorphism with an inverse limit. It is still unclear whether the topology of a...

...

parallelograms properly which illustrate the application of the second isomorphism theorem. Also, drawing the lattice upside down as it's done here (joins...

vector subspace of Rn. This restriction does not unnecessarily limit the isomorphism classes of lattices, but it does limit what satisfies the definition...

for the particular case of order 8, here considered. If there is an isomorphism it should be mentioned and documented since Heisenberg groups are important...

\mathbf {k} _{q}(\mathbf {w} ){\big )}\end{aligned}}} and by the first isomorphism theorem, one has a bijection W / k e r ( φ ) ≃ K q {\displaystyle W/ker(\varphi...

19 November 2013 (UTC) It seems like everywhere else the names of the isomorphisms l r a and s are Greek letters λ {\displaystyle \lambda } , ρ {\displaystyle...

constructs a problem in NPI, however ..." Finally, a problem like graph isomorphism can be a candidate to be a member of NPI, if it is in NP and not known...

take its first Chern class, which lives in cohomology (and, ignoring isomorphism/equivalence, these three point views are the same; see Chern class#The...

or in Makino 1994 (the source cited in M&S), but it follows from the isomorphism ( Z / 2 n ) × ≅ ( Z / 2 ) × ( Z / 2 n − 2 ) {\displaystyle (\mathbb {Z}...

(talk) 02:25, 19 September 2010 (UTC) It's commutative as an operation on isomorphism classes of graphs. It's not commutative as an operation on labeled graphs...

homeomorphism if it has a continuous inverse. Look at this: f is a group isomorphism if either it's 1:1 homomorphism or it has a homomorphic inverse. But...

disambiguate articles at Polymorphism, though the title is not consistent with Isomorphism (crystallography). ― Synpath 17:19, 5 February 2024 (UTC) I like the...

1) depends on the isomorphism chosen between Minkowski space and the space of 2×2 Hermitian matrices. As long as this isomorphism is chosen to be { t...

topological spaces mentioned in this section yields a reflector, not an isomorphism. The "Isotonicity" condition for an operator P(X) → P(X) was used once...

general case, where the circle bundle over M might not be orientable, the isomorphism classes are in one-to-one correspondence with the homotopy classes of...

...

I left the following feedback for the creator/future reviewers while reviewing this article: Just adding more sources does not prove notability or answer...

...

The text ". . . an effective version of the Cantor-Bernstein theorem" as it stood might be misinterpreted if 'effective' was given its usual, non-mathematical...

algebraically closed, it is the unique such curve over ''K'', up to isomorphism.... done Paul August ☎ 16:38, Jun 19, 2005 (UTC) In Almost complex manifold...

organizational fields, this 1983 article discusses three types of institutional isomorphism, or three ways organizations become similar to one another for reasons...

...

category with these algebras as objects and that the uniqueness up to isomorphism of the initial algebra generalizes to the initial object and that many...

here, and a not-very-technical explanation of why this mapping is an isomorphism. —David Eppstein (talk) 06:06, 3 January 2022 (UTC) "More generally the...

structure shows the swapping of points and blocks, and the possible isomorphism resulting in symmetry. For a relation to be symmetric its logical matrix...

instruction set, it seems.) It sounds like what you're describing is a field isomorphism (a subfield is something completely different). My abstract algebra isn't...

there is an entirely different sort of argument that there exists an isomorphism between these two spaces (e.g., by showing that they have the same cardinal...

one and the same if and only if there is no way to tell them apart. Isomorphism is not necessarily identity, nor is equality. These are deep issues and...

...

what this is good for, and the nature of the exciting theorems and isomorphisms that the algebra generates. linas 16:23, 26 November 2006 (UTC) Directly...

is also the map f ↦ d f {\displaystyle f\mapsto df} followed by the isomorphism R ⋅ d x ≅ R ⋅ 1 {\displaystyle R\cdot dx\cong R\cdot 1} . Ozob (talk)...

...

differential forms can have a kernel, but the categorical pullback is an isomorphism of the fibres.151.204.6.171 Linas, regarding the statement: If the map...

...

Spinors are members of a subset of a Clifford alegbra, the subset being in isomorphism with a Clifford algebra corresponding to a lower physical dimension,...

...

an object up to canonical isomorphism in a certain category. The fact that it is only defined up to canonical isomorphism is an important feature of...

so the set of minimal forbidden graphs is finite (all of this up to isomorphism). In the other direction, it's trivial to show that there is no infinite...

This article could use an illustrative example like the one that appears in the Fractional Graph Theory book linked in the References section. J. Finkelstein...

don't name concepts after adjectives, we name them after the noun (e.g. isomorphism, not isomorphic), so "Trivial (mathematics)" would be wrong. Triviality...

...

property (1), Hom(-,X) is an arrow-reversing isomorphism of categories. Further, because it's an isomorphism of categories, X* = Hom(X,X) has the same two...

describing the differential, which is related to the gradient via a musical isomorphism. This discrepancy appears to be confirmed by the content of the article...

around terms like "isomorphism" and "vector space", which are completely unnecessary for a basic definition.   COMMENT: -- isomorphism: yes one could just...

...

(albeit without noting the induced contravariance in the morphisms), up to isomorphism every totally disconnected compact Hausdorff space, or Stone space as...

equality signs (=) all over. Those should instead be something indicating isomorphism rather than equality. An inprovement since i last checked in is that...

ideas can be applied to other classes of finite groups to give every (isomorphism class of) irreducible representation. In this paper we give an affirmative...

Alexandrov topological spaces and preorders when there's an equivalence, even isomorphism of categories? Usually a duality would mean that there's an equivalence...

\mathbb {P} ^{n}} . For $H^{n-1}$ use the long exact sequence to get the isomorphism H n − 1 ( X ; O X ) ≅ H n ( P n ; O X ( − d ) ) {\displaystyle H^{n-1}(X;{\mathcal...

spaces. They are presumably often ignored since several of the concepts (isomorphism, symmetric/alternating/skew-symmetric, associated quadratic form) don't...

something that exists only up to isomorphism, in some sense. There are no distinguished representatives of the isomorphism class that are "natural". Sławomir...

accurate: Note that the isomorphism described above is not unique, and there is no natural choice. Choosing such an isomorphism for a connected groupoid...

the category of sets. As such, the discrete union is defined up to an isomorphism, and the definition with "index space" given in the article is just one...

one of these 42 possible outcomes (up to isomorphism) (https://www.researchgate.net/figure/The-42-isomorphism-types-of-oriented-graphs-of-order-4_fig4_335258169)...

24 (talk) 21:18, 17 February 2009 (UTC) Hello. There is a well known isomorphism between the groups Sp(2) and Spin(3) and also one between Sp(4) and Spin(5)...

that content to the article on heisenberg group) and there's a G-module isomorphism, in the texts I'm reading (mumford), there is no plancks const (its not...

be inaccessible (assuming choice). But an elementary embedding is an isomorphism between models, so if λ isn't inaccessible, what exactly is Vλ being...

infinitely many variables, where Yi is given degree i for all i > 0, one isomorphism being the one that sends Yi to ei ∈ ΛR for every i. The point is that...

that respects the isomorphism. I like to think of Clifford algebras as the core algebraic structure that is preserved by the isomorphism, rather than as...

reference to the statement "was originally introduced much earlier" - isomorphism of problems is seldom straightforward, therefore i thought it is better...

...

well. Locally, a complex structure is equivalent to choosing a linear isomorphism J on each fiber of the tangent bundle such that J 2 = − 1 {\displaystyle...

not hyphens. Fixed. Tokenzero (talk) Why is graph isomorphism mentioned, but not subgraph isomorphism? And this is another paragraph without footnotes...

...

generating sets, add section on appearance of the night sky, explaining the isomorphism between restricted Lorentz group and Moebius group, and its physical...

Boole did not discover any isomorphism or model theoretic relation between the propositional connectives and his eponymous algebra, because those connectives...

no sense unless you specify what structures are isomorphic: is it an isomorphism of vector spaces, of Lie algebras, or of some other structure (also it...

not hyphens. Fixed. Tokenzero (talk) Why is graph isomorphism mentioned, but not subgraph isomorphism? And this is another paragraph without footnotes...

fundamental metric concept is short map, the morphisms of the metric category (isomorphisms, i.e. bishort maps, are the isometries), but its usual expresion uses...

stalks are "equal", does that mean they are literally equal? or up to an isomorphism? F x = F y {\displaystyle {\mathcal {F}}_{x}={\mathcal {F}}_{y}} ? Or...

no tensors in this business. They come in only by identifications and isomorphisms. This theory is developped in a completely basis-free way in terms of...

is isomorphic to the usual multiplication on the complex plane, the isomorphism given by complex conjugation. perkinsrc008 12:19, 14 April 2008 (UTC)...

March 2006 (UTC) Modular arithmetic Modulo operation Quotient group OK Isomorphism theorem#Rings and modules modulo/modulus not mentioned Group (mathematics)...

emerged has argued that institutions have developed to become similar isomorphism across organizations even though they evolved in different ways, and...

March 2023 (UTC) From Google Gemini: Clarifying Isomorphism and Topological Properties: Isomorphism in the context of fields refers to structural equivalence...

should be deferred to the subpage. As for the isomorphism: I don't know why I called this adjunction isomorphism, since it is effectively both adjunction and...

smooth inverse. It will also turn out to be an isomorphism of groups, so that it is actually an isomorphism of Lie groups. Hope that helps. -Lethe | Talk...

here). I think it is really easy like PSU(2,q^2)=SL(2,q) or so, and the isomorphism is natural for all commutative rings with involution, not just the finite...

for oriented CW-complexes? If not, why does a set of choices of these isomorphisms with spheres not affect the resulting homology of the complex? Or does...

The sentence starting "In abstract algebra, the real numbers are up to isomorphism uniquely characterized", this is confusing to me (I think may be a slip...

the continuum with the η1 property. (Such a structure is unique up to isomorphism, assuming the continuum hypothesis.) How to construct it explicitly is...

(Albert and Sandler) that gives them in this form (up to an alphabetic isomorphism). Bill Cherowitzo 04:28, 21 September 2011 (UTC) — Preceding unsigned...

have inverses relative to an identity. The notions of homomorphism and isomorphism so crucial to abstract algebra should also be expanded upon, preferably...

some results on module theory over a Dedekind domain, in particular the isomorphism from the class group to reduced K_0. (iv) some other miscellaneous results:...

What is its identity element and group operation then? And what is the isomorphism between these sets? I believe the author meant Q / { 0 } {\displaystyle...

from V*⊗W to L(V,W), which is an isomorphism for finite dim. In infinite dimensional spaces there is no isomorphism, but there is still a natural injection...

passage: "All finite fields of the same order are isomorphic, so, up to isomorphism, there is only one finite projective space for each dimension greater...

to isomorphism) within each ('standard' or not) model of ZFC. That is what categoricity means. You can't even define the same kind of an isomorphism between...

In the section on properties it states that pullbacks preserve isomorphisms. However, the supplied references only support that retractions are preserved...

*-homomorphism between C*-algebras is isometry." Should that be a *-isomorphism? 76.126.116.54 (talk) 04:03, 12 March 2009 (UTC) Maybe I should stop...

The parenthese "(ring-)" was here (I guess) for emphasizing that the isomorphism does not extend to other properties. I have fixed the mathematical accuracy...

cdoordinates.83.104.131.53 12:44, 5 February 2006 (UTC) It says that there's an isomorphism between J p k ( R n , R m ) {\displaystyle J_{p}^{k}({\mathbb {R} }^{n}...

gloss but I'm not certain I got it right. This also affects Cantor's isomorphism theorem which has a similar paragraph (that I reused here to replace...

product operations may be different. The vec operator is a vector space isomorphism. from K p × q {\displaystyle \mathbb {K} ^{p\times q}} to K p q {\displaystyle...

on the one hand *THE* random graph is certain specific (unique up to isomorphism) graph with an infinite number (more specifically ℵ 0 {\displaystyle...

But when direct sum and when outer product should be used to indicate isomorphism. Koeplinger 12:16, 1 April 2007 (UTC) The two products ⊕ {\displaystyle...

the real "structure" consists of an object in graph theory, and the isomorphism is set up by corresponding vertices of the directed graph to possible...

{\displaystyle f} has inverse f − 1 {\displaystyle f^{-1}} then map f is an isomorphism. in Haskell foldr and unfold, may be defined as follows: foldr op e =...

fundamental isomorphism and involved dimensions. Link this to the first example. State and emphasize that dim V characterises V up to (non-unique) isomorphism, and...

bundle map articles, but also to clarify a few points, such as bundle isomorphism and trivialization. There is clearly still work to be done here though...

it doesn't state that a homomorphism must preserve identity (only an isomorphism) and leaves it as an exercise to construct an example to illustrate....

explain what distinguishes cold pressing from other methods of juicing.GreenIsomorph (talk) 09:00, 10 May 2017 (UTC) The current definition of cold pressed...

–jacobolus (t) 09:12, 30 May 2026 (UTC) I changed the lead to remove "isomorphism" early on because it seemed to me that belaboring this rather fussy point...

systems based on higher-order typed lambda calculus through a Curry–Howard isomorphism, cut elimination algorithms correspond to the strong normalization property...

of induction or analogy, what combination of metaphors constitutes an isomorphism, mathematicians' social capital and the meaning of the well-known collaboration...

(connected, I guess) reductive Lie group also. In other words local isomorphisms allowed. Charles Matthews 13:45, 14 September 2006 (UTC) Having finitely...

section. In addition, there are undefined technical terms (e.g., anti-isomorphism is neither defined nor linked elsewhere). The article is mostly factually...

-1. John Baez (talk) 19:06, 4 February 2008 (UTC) And what about the isomorphism of PSL(2,3) with PSL(7,2), the simple group of order 168 ?— Preceding...

remain unclear for me. The structure of O±(2, q): I unable to provide an isomorphism with the dihedral group. It seems that the number of elements relies...

naturally isomorphic to", as the article states, hence the link to natural isomorphism. Dependent Variable (talk) 20:19, 24 September 2009 (UTC) Is this correct...

proof as given in the article is correct: TSP "is" (up to some kind of isomorphism) JSP with one machine, and TSP is an NP problem... in fact, it is NP-complete...

topos from intuitionistic type theory yields two truth values (up to isomorphism), i.e. two global elements of the subobject classifier, namely true and...

{\displaystyle B} and A {\displaystyle A} , and want to classify these up to isomorphism — that's a reasonably natural thing to do, even for a reader who does...

"lumped systems" (ex. of the Mechanical-electrical analogies)... See also Isomorphism. --Krauss (talk) 08:13, 16 December 2014 (UTC) (section moved from original)...

symmetric tensors into the symmetric tensor algebra. However this is not an isomorphism in general (e.g., over fields of prime characteristic). Sławomir Biały...

make an assumption. You choose an isomorphism between these vectorspaces. Or equivalently you have chosen isomorphisms from R^2 to each of those vectorspace...

Neukirch at hand, so I can't verify whether he indeed calls the main isomorphism of the global class field theory "the Artin reciprocity law". Nonetheless...

also vector space isomorphisms between them. These are all equivalent to multiplying by a non-zero scalar and applying a field isomorphism. Multiplying by...

cofibrant replacement, and this is actually well-defined up to unique isomorphism (I think?) in the derived category. Any thoughts? Dave Rosoff 04:10,...

I'm just trying to understand this algorithm so please excuse me if I'm mistaken but I think the labeling in this image is wrong for node A on the right...

with one object such that every nonzero morphism of the category is an isomorphism"? Or perhaps it doesn't need to be mentioned in the lede. Michael Slone...

Done. —David Eppstein (talk) 23:49, 10 August 2023 (UTC) Finally, link Isomorphism just to be on the safe side. Done. —David Eppstein (talk) 23:49, 10 August...

I left the following feedback for the creator/future reviewers while reviewing this article: Please add the publication details for the Muhlherr reference...

without explaining just what the hell it is all about. Todd class, Thom isomorphism, Chern class, etc. aren't mentioned --euyyn 08:20, 23 April 2007 (UTC)...

Reals in Projective Geometry and proving that the Reals are unique up to isomorphism. Updated link for John Nachbar "Numbers" https://bpb-us-w2.wpmucdn.com/sites...

the complex version. This doesn't fit the definition given for "anti-isomorphism" in the linked article. Perhaps it should say "anti-isometric" instead...

...

following adjunction in cartesian closed categories: There is a natural isomorphism between the morphisms from a binary product f : ( X × Y ) → Z {\displaystyle...

generalizations of the standard theory of two player games and the well known isomorphism between sentences written in prenex normal form and games. I'm not saying...

as brokerage, strength of weak ties, structural holes, influentials, isomorphism, etc., are not defined anywhere on wikipedia. They all deserve their...

graph with diameter 2, girth 5, and degree 57, then it is unique up to isomorphism. However, it is possible that there exists non-isomorphic such graphs...

themselves: there's an obvious crossover in parties, (tho' it's not an isomorphism). So I'll live with it until the PACE groups get sorted out. Regards...

product. I guess that the fundamental theorem is nothing else than the isomorphism theorem for vector spaces. I have tagged the article for warning the...

gameplay is what the single Hamiltonian cycle on the dodecahedron (up to isomorphism) looks like and how to remember it. I think that's not really much more...

group of order 8 and D_8 is the dihedral group of order 8). We have isomorphisms everywhere but D_8 and Q_8 (1 -> 1 is both epi and mono). Thus this FAILS...

more related to what mathematicians call "equality up to a canonical isomorphism" than to this article. D.Lazard (talk) 15:25, 30 September 2015 (UTC)...

to do with directed graphs (so their should be more subgraphs up to isomorphism...). ConcernedScientist 19:01, 30 May 2007 (UTC) I have yet to see one...

time I use it, so I can't remove it. As for point 1: It's true that an isomorphism between a vector space and a coproduct of the field is equivalent to...

algebraischen Zahl- und Funktionenkörpern formulated what are now called the isomorphism theorems, describing a set of natural transformations. Key to these theorems...

use to represent the equivalence class of a total order under order-isomorphism? For well-orders, we have the von Neumann ordinals as archetypes. But...

is that Kuratowski's theorem says there exists such an isomorphism. Whether this isomorphism is constructible, I don't know. Should I worry sone more...

defines a set with the appropriate "Peano structure" uniquely up to isomorphism. It can now be shown that for this set the proposition usually called...

Fields. I have said let's not to talk about isomorphism. Especially, "isomorphism" is called "isomorphism", is not called "synonym". If two structures...

V^{*}\;} and V ¯ {\displaystyle {\overline {V}}} is the nature of the isomorphism. In particular, I think the dual V ∗ {\displaystyle V^{*}\;} is in some...

something ? I think the usual theorem states that this is supposed to be an isomorphism of R-algebras. EHecky (talk) 17:20, 20 March 2023 (UTC) By definition...

coordinate system on a space is a collection of coordinates which provide an isomorphism of an open subset of the space with an open subset of Rn where R is the...

involved deeper math­e­mat­ics related to permutation groups and the graph isomorphism problem.)" does not need the parenthesis IMO.  Not done As before, it's...

that is not used outside coding theory. I guess that "isomorphism mapping" means "field isomorphism". Apparently, the problem that you consider is to present...

between a set and itself (trivial, of course). [analogy: isomorphisms between two groups and isomorphisms from a group onto itself.] perhaps this should be clarified...

what KharanteDeux wrote. The truth is that the inner product induces an isomorphism between a vector space and its dual, that allows identifying vectors...

on Euclidean 3-space". These are two different isomorphisms (I have not verified your claimed isomorphism, but its validity is irrelevant anyway). Please...

anyone have an idea where I can find more and better sources about the isomorphism between the arithmetic of numbers of the form ⁠ a + b φ {\displaystyle...

abelian quasigroup is isotopic to an abelian group, unique in the sense of isomorphism (Theorem 11). This result is essentially Murdoch's." 86.127.138.234 (talk)...

"Monotone Galois connections can be viewed as a generalization of order-isomorphisms, since they constitute of a pair of two functions in converse directions...

the corresponding elliptic curves are isomorphic" And conversely! "The isomorphism classes can be understood in a simpler way..." "Simpler" is POV. "The...

comment for the labeling of the counterexample figure in the "Diamond isomorphism theorem" section, where we have x≤b, rather than a≤b. These notational...

value, this encoding is interesting for the fact that it provides an isomorphism between the binary relations of integers under the bit predicate and...

BCK-Algebras, a usual, but very indirect, relation. see Curry-Howard isomorphism. So BCKW-Algebra means Hilbert Algebra. see implication algebras. DefLog...

here, and a not-very-technical explanation of why this mapping is an isomorphism. —David Eppstein (talk) 06:06, 3 January 2022 (UTC) "More generally the...

the normal subgroup 23. An interesting consequence of the exceptional isomorphism between GL(3,2) and PSL(2,7). — Preceding unsigned comment added by Scott...

=-\Phi ^{2}} . (For a proof consider the projective isomorphism f ( z ) = a z + b c z + d {\displaystyle f(z)={\frac {az+b}{cz+d}}} with...

context of vectors, Bourbaki does not state it as an isomorphism, but as a homomorphism with isomorphism in the finite-dimensional case: http://books.google...

contains broken links to one or more target anchors: [[Johnson solid#isomorphs]] The anchors may have been removed, renamed, or are no longer valid....

arbitrary as a symbol, but acquires its allusive power from an isomorphism (though I knew "isomorphism" wasn't the right term either). So I came to Reference...

gameplay is what the single Hamiltonian cycle on the dodecahedron (up to isomorphism) looks like and how to remember it. I think that's not really much more...

Similarly, all instances of "X/ker (f) \cong im(f)" should be centered in Isomorphism theorem and so on. Jakob.scholbach (talk) 16:47, 20 June 2008 (UTC) This...

others: ... Now do these properties describe the structure uniquely (up to isomorphism)? Obviously not since for structure (2) the above properties hold as...

concrete vector space k n for each n. In both cases these are, up to isomorphism, the only finite/finite-dimensional such. (That the only non-free algebras...

isomorphism theorems ? — Rgdboer (talk) 00:36, 30 October 2024 (UTC) I'm not too familiar with them. From the introductory sentences at Isomorphism...

(UTC) A note: I know lambda-calculus and have read about Curry-Howard isomorphism, but I'm not at all an expert in the subject (particularly, in the calculus...

between isomorphism and equality is also irrelevant here. Perhaps David should have said "is isomorphic to" rather than "is", because the isomorphism might...

say 'Cn is isomorphic Z/nZ', because how are you supposed to have an isomorphism when you haven't even told me what the elements of Cn are? This is something...

co-ordinate transformations on hyperbolic surfaces in 3d through the isomorphism with Cℓ01,2(R). Seeing Cℓ1,1(R), one can read off immediately that this...

Dedekind-completeness). Indeed, from the page Real_number, up to field-isomorphism, the reals are unique as the only totally ordered field, complete and...

especially matroid isomorphisms, 3) more rigorously define matroid representability using matroid morphisms, 4) describe isomorphism classes for small...

a morphism from A to B. A gluing is a tuple (A, m, B) where m is an isomorphism. A C-manifold is an (equivalence class) of a set of gluings. Of course...

leftmost-possible paranthezation, this "identification" just employs an isomorphism similar to my above example. — I'll try to come up with a note along...

All of these perspectives are connected by a "natural isomorphism" (that is, an isomorphism that does not require any choices to be made or additional...

to have different cycle graphs. Further, this would give just eight isomorphism classes of non-Abelian groups of order 16, meaning we're missing one...

is that they are equivalence classes of well-orders with respect to isomorphism, but I would imagine that is even more abstract.) It also gives a representation...

course the total spaces are diffeomorphic. However there is not a natural isomorphism between them, unless you have some additional structure such as Riemannian...

the creation of specialisations (such as the I Ching). This elicits isomorphism of specialisations. (4) what this does is allow for the ease in making...

is wrong with the caption? The article also does not talk about graph isomorphism explicitly, so I believe this image can complement it. --xJaM 10:20,...

ideals on sets, such as take products of them and ask about Rudin-Keisler isomorphisms, that don't obviously generalize to the other sorts of ideals. Ideals...

care to specify the type of isomorphism. If we are referring to a ring isomorphism, what you say gets confused by isomorphism of distinct signatures. If...

in the case of non-propositions. I know there's some kind of common isomorphism with boolean algebra in the background here, but I can't see how to use...

but then the computational difficulty shifts to the computation of the isomorphism. Traditionally this article has not dealt with the easy cases, because...

hnh−1∈N since N is normal in G.) Together N, H and φ determine G up to isomorphism, as we show now." But the section immediately continues by defining the...

second-order language of arithmetic that completely determine the model up to isomorphism, and therefore completely determine truth in the standard model, when...

(viewing a group as a miniature category with just one object and only isomorphisms)." One would think that putting the part in parentheses: "(viewing a...

of the dot product is (as you said originally) preserved under every isomorphism, for that definition of an isometry to make sense, the dot product has...

vectors are collections of scalars, after all—if one does not mind an isomorphism. On an (personally, admittedly) cursory inspection, the section appeared...

proofs such as "By abstract nonsense, tensor products are unique up to isomorphism when they exist". The joke got old and survives only vestigially in the...

i.e., hacking. Based on this I found P. Wadler (1993), "Curry-Howard isomorphism for Sequent Calculus", a private communication which is citation #13...

operations of addition and multiplication makes the two isomorphic - See Isomorphism. To mathematicians, two isomorphic fields (or any other relevant structures)...

the motivation lies in his general attempt to put Babbitt's pitch/time isomorphism on sound theoretical footing.) Second, in the claim that the identity...

{C}};q_{1},\ldots ,q_{n};{\tilde {f}})} are isomorphic if there is an isomorphism of curves τ : C → C ~ {\displaystyle \tau :C\to {\tilde {C}}} taking...

...

the same point as BlockArranger. Just because someone has explored the isomorphism between a doughnut and a coffee cup, it doesn't mean doughnuts should...

{\displaystyle S(a)\cup S(b)=S(\max(a,b))} As far as I know, this is an isomorphism, so quite a bit more than an analogy, and might not necessarily help...

configuration of a collection of minutae about an individual and physiognomic isomorphism.DrJohnGPhD (talk) 17:10, 14 November 2012 (UTC) I have removed the reference...

maps. 5. The statement regarding the first isomorphism theorem isn't completely right. The first isomorphism theorem gives us that the image of D y f {\displaystyle...

thing for any historical background would be to establish whether the isomorphism C(r,s) ≅ O(r+1,s+1) [Hestenes 2009 [12], eqn. 16] -- i.e. between the...

Gordon and Breach Science Publishers While other sources also assert this isomorphism (as seen in the Möbius group article), the assertion would imply that...

space, then T : X → X ∗ ∗ {\displaystyle T:X\to X^{**}} is an isometric isomorphism an the initial topology with respect to it therefore produces the norm...

This follows from the fact that the transition functions are linear isomorphisms (or that the structure group is GL(n)). Compare definitions 1 and 2 in...

q-r+1}^{r}\circ d_{p,q}^{r}=0} , called boundary maps or differentials; 3. Isomorphisms of E p , q r + 1 {\displaystyle E_{p,q}^{r+1}} with H ( E p , q r ) {\displaystyle...

bilinear form can satisfy f(x,y)=0 for all y only if x=0 without being an isomorphism, and therefore doesn't satisfy the criteria for a non-degenerate form...

group of order 15. Thus, there is only one group of order 15 (up to isomorphism)." Just because you have two subgroups of trivial intersection who's...

right), see: Jochen Burghardt, Florian Kammüller, Jeff W. Sanders (2000). Isomorphism of Galois Embeddings (Technical report). GMD. p. 73. ISSN 1435-2702....

solution to Hilbert 5 trivially implies that the definition by "local isomorphism to a linear Lie group" works. And it is much more standard and useful...

factor.) I guess an alternative definition, which avoids these tricky isomorphism issues, is to say that K is an internal direct factor if it is one of...

overall influence. Phlsph7 (talk) 17:57, 11 March 2024 (UTC) I think isomorphism needs some treatment in "Universal algebra", the key being: it is a type...

one-to-one correspondence that preserves the algebraic properties is an isomorphism. And said in the introduction that an isomorphic representation of the...

the n-parallelotope is the image of the unit n-hypercube by the linear isomorphism that sends the canonical basis of R n {\displaystyle \mathbf {R} ^{n}}...

Please note that I did not ask for a classification of fields up to isomorphism. But there should certainly exist some classification of the different...

Morten Heine; Urzyczyn, Paweł (2006) [1998], Lectures on the Curry–Howard isomorphism, Studies in Logic and the Foundations of Mathematics, vol. 149, Elsevier...

discipline is usually important, it is common to seek values "up to isomorphism" and the isomorphism between scalars and 1×1 matrices justifies this. — Ezrakilty...

knew something about algebra. There is only one two-element field up to isomorphism, and the tables of its operations are forced by the field axioms (0 is...

connected covering space with a canonical smooth structure and (up to isomorphism) a canonical group structure making it a Lie group called the universal...

the cube and the octahedron but this seems to contradict the Whitney isomorphism theorem. From some quick doodling I seem to find that the edge graph...

(UTC) What is meant by $Spin(2)=U(1)$ and te others? Surely they are not isomorph as topological groups, since $Spin(2)$ as to be simply connected, while...

clear definition is needed. Symmetry group doesn't address the matter of isomorphism over and above describing particular groups as isomorphic to abstract...

a non-free monoid as a quotient of a free monoid. You get additional isomorphisms that correspond to two words being "equal" in the quotient. — Preceding...

02:39, 3 July 2011 (UTC) It says "In order to interpret Φ as a natural isomorphism, one must recognize homC(F–, –) and homD(–, G–) as functors. In fact...

uniqueness" is the statement "The object A itself is only unique up to isomorphism." It makes sense that in the category of morphisms from X to U that the...

the one generated by projective transformations, such as birational isomorphism? —David Eppstein (talk) 17:37, 15 October 2025 (UTC) I think I see the...

{\displaystyle f} and g {\displaystyle g} are isomorphisms then f ∘ g {\displaystyle f\circ g} is also an isomorphism", make unnecessary to mention the range...

obviously be the set of all blocks of the partition induced by the order-isomorphism equivalence w ~ w'. If that's what you meant, we're on the same page...

theorem: this quotient group G acts transitively on PH and so there is an isomorphism between the group and the space of pure states. Don't we need the group...

for authoritative definitions. Rotations in pseudo-Euclidean spaces. Isomorphism between SO+(1,3) and the Möbius group. They are not compact, but include...

the von Neumann universe, which is well-specified up to a canonical isomorphism, and which can be described in an intuitively clear way without starting...

and of an orthonormal basis on it associated vector space induces an isomorphism (of Euclidean spaces) between the given Euclidean space and R n {\displaystyle...

Quartic is widely documented and well established as the limit of possible isomorphs on a 3D surface, and the human brain is equally well established as an...

function. The message here is that being a RKHS is not preserved by isomorphism. Also, I should point out that the delta function is not a function in...

sets are identical "up to an isomorphism" ((in French)à un isomophisme prêt) - we can find a similar expression in isomorphism#Relation with equality. TomT0m...

(talk) 12:14, 22 June 2009 (UTC) Hi! It is stated that we have (up to isomorphism) independence of the base point provided the space in question is path-connected...

occurs: Restricted to unit quaternions, this representation provides an isomorphism between S3 and SU(2). This sentence has the problem that technically...

thus it is appropriate to talk about the symmetric group Sym(M) (up to isomorphism)." If M is finite and a group G of permutations of M is isomorphic to...

Lagrangian intersection Floer theory. I add a subsection titled PSS isomorphism in order to obtain the equivalence between Floer homology and the ordinary...

of measurement and scale as it is. Stevens (1946, p. 677) said: "The isomorphism between ... properties of the numeral series and certain empirical operations...

unless you are willing to break the usual rules of what is meant by isomorphism. Silly rabbit 20:45, 24 May 2007 (UTC) An even more clear-cut example...

February 2010 (UTC) Correction. A proof has been supplied to show the isomorphism with C ⊕ C {\displaystyle C\oplus C} . Dialogue welcomed here in Talk:Tessarine...

to: The subsections on various kinds of numbers under "Equality vs. isomorphism" are all poorly written, very muddled, and very dubious/controversial...

"Hybrid Systems Methodology: Tests for Hierarchy and Linkages Between Isomorphisms", in: Cybernetics and Systems Research 2, ed. R. Trappl, pp.39-45, North-Holland...

2019 (UTC) hum added by Haldolhaldol (talk) 15:23, 8 September 2009 (UTC) Isomorph (band) Hilary Jeffery added by Hoof Hearted (talk) 12:24, 25 September...

explanations. These have been linked to: half-reaction, electron configuration, Isomorphism (crystallography), isostructural, coordination complex (reworded slightly)...

Of course there is a relation between those objects (and indeed an isomorphism between the spaces conataining them), but both articles should definitely...

observation is in the abstract of Bodlaender, "Polynomial algorithms for graph isomorphism and chromatic index on partial k-trees", SWAT 1988, and earlier in Bodlaender's...

the group law in terms of the symplectic form. The second bit, the isomorphism between the coordinate free approach and the matrix approach, where I...

space, but also the distance function, topology, etc. Then, up to an isomorphism, there is precisely one 3D Euclidean space. Saying "any 3D Euclidean...

A and B that are not equal, with an isomorphism F from A to B, we can take the statement φ(X): F is an isomorphism from X to B. If A and B were equal,...

product is linear in the first argument, and it is an antilinear isomorphism, not an isomorphism. Anyway, I think requiring it to be an iso is too strong because...

However there are uncountably many such isomorphisms between any two such spaces. What distinguishes the isomorphism that brings these two wave functions...

{g}}/{\mathfrak {h}}} at x) is an isomorphism, so the model spaces are "tangent" to M in some sense. This isomorphism is called a "solder form" in physics...