Arrow category
= Arrow category
{title2=$[\mathbf 2,\mathcal C]$}
The arrow category of $\mathcal C$ has morphisms $A_0\to A_1$ of $\mathcal C$ as objects and commutative squares as morphisms. It is the <functor category> $[\mathbf 2,\mathcal C]$, where $\mathbf 2$ is the category with one nonidentity arrow.
It is also the <comma category> $(\operatorname{id}_{\mathcal C}\downarrow\operatorname{id}_{\mathcal C})$.