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namely that there is a set of morphisms between any two objects).

To get the dual concept of quotient object, replace "monomorphism" by "epimorphism" above and reverse arrows. A quotient object of A is then an equivalence class of epimorphisms with domain A.

However, in some contexts these definitions are inadequate as they do not concord with well-established notions of subobject or quotient object. In the category of topological spaces, monomorphisms are precisely the injective continuous

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