Remark 78.20.4. 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 78.20.3 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 78.22) and that it is close to being a $2$-coequalizer of $s$ and $t$ (Section 78.23).

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