Kerodon

Remark 5.3.4.5 (Isomorphism Invariance). In the situation of Definition 5.3.4.2, suppose that we are given a pair of morphisms $\lambda , \lambda ': \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} ) \rightarrow \operatorname{\mathcal{E}}$ which are isomorphic when viewed as objects of the $\infty $-category $\operatorname{Fun}_{ / \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}}) }( \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} ), \operatorname{\mathcal{E}})$. Then $\lambda $ is a scaffold if and only if $\lambda '$ is a scaffold (see Corollary 5.1.2.5 and Remark 4.5.1.15).