Kerodon

Remark 7.7.2.4 (Isomorphism Invariance). In the situation of Notation 7.7.2.1, suppose that $\operatorname{\mathcal{C}}$ is an $\infty $-category. Then the condition that $F: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is an effective descent diagram for $U$ depends only on the isomorphism class of $F$ (as an object of the $\infty $-category $\operatorname{Fun}( K^{\triangleright }, \operatorname{\mathcal{C}})$). This follows from the characterization given in Remark 7.7.2.3 (together with Corollary 7.1.3.14).