Kerodon

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6.4 Tags Lost in Reorganization

These tags became irrelevant because they refer to an older organization of various materials.

Remark 6.4.0.1. Let $S$ be a simplicial set, and let $(\operatorname{Set_{\Delta }})_{/S}$ denote the slice category of simplicial sets $X$ equipped with a morphism $q_{X}: X \rightarrow S$. Then we can regard $(\operatorname{Set_{\Delta }})_{/S}$ as a simplicially enriched category, with mapping simplicial sets given by

\[ \underline{\operatorname{Hom}}_{ ( \operatorname{Set_{\Delta }})_{/S} }( X, Y) = \operatorname{Fun}_{S}(X,Y). \]

Remark 6.4.0.2. For relative versions of Corollaries 4.3.6.7 and 4.3.6.9, we refer the reader to §8.0.1.

Remark 6.4.0.3. In the special case $S = \Delta ^{0}$, Proposition 4.3.6.5 reduces to Corollary 4.3.6.7, Corollary 4.3.6.6 reduces to Proposition 4.3.6.1, and Proposition 4.3.6.8 reduces to Corollary 4.3.6.9.