Arrow category

The arrow category $𝖢 \to$ of a category $𝖢$ has morphisms of $𝖢$ as objects, and for $𝑓 \in 𝖢 (𝑋, 𝑌)$ and $𝑓' \in 𝖢 (𝑋', 𝑌')$ a morphism $𝑔 \in 𝖢 \to (𝑓, 𝑓')$ is a pair of morphisms $𝑔 1 \in 𝖢 (𝑋, 𝑋')$ and $𝑔 2 \in 𝖢 (𝑌, 𝑌')$ such that the following diagram commutes:¹ cat