In a category $\displaystyle \mathcal{C}$ a subobject of an object $\displaystyle A$ is an object $\displaystyle B$ such that there exists a monic $\displaystyle \phi : A \longrightarrow B$. Simple enough.

But I need to show that if $\displaystyle A$ is a subobject of $\displaystyle B$ and $\displaystyle B$ is a subobject of $\displaystyle A$, then $\displaystyle A = B$.

It looks obvious but I think I am missing something.