In a category a subobject of an object is an object such that there exists a monic . Simple enough.

But I need to show that if is a subobject of and is a subobject of , then .

It looks obvious but I think I am missing something. (Wondering)

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- Nov 22nd 2009, 03:03 AMpercimbeSubobjects in a category
In a category a subobject of an object is an object such that there exists a monic . Simple enough.

But I need to show that if is a subobject of and is a subobject of , then .

It looks obvious but I think I am missing something. (Wondering) - Nov 22nd 2009, 03:43 AMpercimbe
Ah, If is the other monic then their composition is monic, but their compositions are identity morphisms for A and B; and . Hence they are isomorphic! Or is there a strict equality? (Thinking) help