Kerodon

Remark 10.3.0.9. In §10.3.2, we adopt a slightly different definition of quotient morphism (Definition 10.3.2.1), which makes sense in any $\infty $-category $\operatorname{\mathcal{C}}$ (that is, we do not need to assume that $\operatorname{\mathcal{C}}$ admits pullbacks). Our definition is formulated using the language of sieves, which we review in §10.3.1. When $\operatorname{\mathcal{C}}$ admits pullbacks, the sieve-theoretic definition reduces to the requirement that $\operatorname{\check{C}}_{\bullet }(X/Y)$ is a colimit diagram (see Proposition 10.3.2.4).