ScalingStacks

Remark 5.2. By Lemma 3.5 $\gaunt_{n}$ is locally finitely presentable. It follows (see [1, Corollary 2.44, 2.47]) that each of the categories of $k$-correspondence is also locally finitely presentable.

Given two $k$-correspondences $M\to C_{k}$ and $N\to C_{k}$, we may form the product correspondence $M\times_{C_{k}}N$. This is the product in the category $(\gaunt_{n}/C_{k})$ of $k$-correspondences.