Nerve of an ∞-category

Definition 24.1.1 (Nerve). The nerve of an \(\infty \)-category \(C\) is the simplicial anima \(N(C) \colon \simp \catop \to \An \) defined by \(N(C)_n := \Map ([n],C)\), i.e. as the composite \[ \simp \catop \hookrightarrow \Cat \catop \hookrightarrow \Cat _{\infty }\catop \xrightarrow {\Hom _{\Cat _{\infty }}(-,C)} \An . \] This construction is functorial in \(C\) and thus defines a functor \(N\colon \Cat _{\infty } \to \sAn \).