Associated ∞-category of a simplicial anima

Construction 1.8.11 (Associated \(\infty \)-category). Every simplicial anima \(X\colon \simp \catop \to \An \) has an associated \(\infty \)-category \(\ac (X) \in \Cat _{\infty }\). To construct it, consider the inclusion \(\simp \hookrightarrow \Cat _{\infty }\) from Axiom L. By Theorem 1.8.9, this uniquely extends to a colimit-preserving functor \[ \ac \colon \sAn = \PSh (\simp ) \to \Cat _{\infty }. \] In particular, every simplicial set \(X\) (hence every quasicategory) defines an \(\infty \)-category \(\ac (X)\) by regarding it as a simplicial anima via the inclusion \(\sSet \hookrightarrow \sAn \).