19 Jun
2003
19 Jun
'03
12:52 p.m.
Let me just add to this reply (which is certainly one valid answer to the question) the comment that I sent privately to the questioner that exactness is sufficient for the FIT to be meaningful. On Thu, 19 Jun 2003, Toby Bartels wrote:
Andrei Prokopiw wrote:
Is there a suitable first isomorphism theorem in category theoretic language? One barrier for me seems to be the correct notion of an image. What seems best right now would be that given f:X->Y, ker(coker f) = coker ( ker f). Here the left hand side would represent im f, and the right hand side X/kerf. If this is the right notion, what are the necessary conditions on the category for it to hold?
I'm not really answering your question, instead addressing the "if".
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