Kerodon

Remark 4.5.1.4. Let $\mathrm{h} \mathit{\operatorname{Kan}}$ denote the homotopy category of Kan complexes (Construction 3.1.5.10). Then we can regard $\mathrm{h} \mathit{\operatorname{Kan}}$ as a full subcategory of the $\infty $-category $\mathrm{h} \mathit{\operatorname{QCat}}$ (Construction 4.5.1.1), spanned by those $\infty $-categories which are Kan complexes. This follows from the observation that if $Y$ is a Kan complex, then a pair of morphisms $f,g: X \rightarrow Y$ are isomorphic as objects of the $\infty $-category $\operatorname{Fun}(X,Y)$ if and only if they are homotopic (Proposition 3.1.5.4).