Remark 77.20.4. In future chapters we will use the ambiguous notation where instead of writing $\mathcal{S}_ X$ for the stack in sets associated to $X$ we simply write $X$. Using this notation the diagram of Lemma 77.20.3 becomes the familiar diagram

In the following sections we will show that this diagram has many good properties. In particular we will show that it is a $2$-fibre product (Section 77.22) and that it is close to being a $2$-coequalizer of $s$ and $t$ (Section 77.23).

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