Thread: Subobjects 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.

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? help