Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$

Corollary 4.1.3.3. Let $X$ be a simplicial set. Then there exists an inner anodyne morphism $f: X \rightarrow Q(X)$, where $Q(X)$ is an $\infty$-category. Moreover, the $\infty$-category $Q(X)$ (and the morphism $f$) can be chosen to depend functorially on $X$, in such a way that the functor $X \mapsto Q(X)$ commutes with filtered colimits.