# Can there be more than one zero morphism between two objects? [duplicate]

Possible Duplicate:
Category with zero morphisms

Given two objects $X,Y$ in a category, can there be more than one zero morphism $X\rightarrow Y$?

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## marked as duplicate by Zhen Lin, sdcvvc, William, Thomas, J. M.Sep 24 '12 at 10:30

In the absence of a zero object, stupid things can happen. For example, consider the category $\{ \bullet \rightrightarrows \bullet \}$ with exactly two parallel non-identity arrows. It is essentially vacuous that both of the non-identity arrows are constant and coconstant – but they are distinct by hypothesis.