Talk:Zero morphism

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I don't feel the courage to define ring and group morphisms, and I think the categoric characterization is too much for most readers. David.Monniaux 22:39, 17 Sep 2003 (UTC)

just redirect them to ring and group homomorphisms. wshun 22:41, 17 Sep 2003 (UTC)

Wshun is right; no need to define here, just link. But all of the links to this page are already talking about category theory, so we should be able to put that in here. In fact, I'd put the examples from algebra (groups and rings) at Zero homomorphism instead. -- Toby Bartels 11:50, 28 Sep 2003 (UTC)

A morphism is zero if and only if it is constant and coconstant.

I can't find the defintion of constant morphism under Constant morphism. It justs says:

The first characterization of constant functions given above, is taken as the motivating and defining property for the more general notion of constant morphism in Category theory.

—Preceding unsigned comment added by JanCK (talk • contribs) 19:34, 20 October 2007

I've now fixed this, as constant morphism is now defined in the article. Paul August ☎ 18:04, 25 January 2010 (UTC)Reply

I suspected constant=left zero but didn't have access to Herrlich-Strecker. Thanks. RobHar (talk) 19:19, 25 January 2010 (UTC)Reply

Glad to help. Paul August ☎ 23:06, 25 January 2010 (UTC)Reply

Can someone write explicitely whether a category with zero morphism necessarily or not necessarily has a zero object? (not quite grammatically correct but you understand) — Preceding unsigned comment added by Noix07 (talk • contribs) 19:04, 6 April 2014 (UTC)Reply

As defined in this article, no, one can consider the category with only 2 objects 0 and 1 and only one non-trivial morphism (0,1) from 0 to 1. That morphism is a zero morphism, but nor 0 nor 1 are zero objects Osci Tienal (talk) 17:10, 28 October 2024 (UTC)Reply

The "Related concepts" section says:

If a category has zero morphisms, then one can define the notions of kernel and cokernel for any morphism in that category.

I don't think C having zero morphisms automatically implies C has kernels / cokernels. But maybe this is not what the text meant to imply? Luca.defeo (talk) 13:02, 29 April 2024 (UTC)Reply