Geometric realization of simplicial objects

Definition 1.7.19. Let \(C\) be an \(\infty \)-category, and let \(X\colon \simp \catop \to C\) be a simplicial object. The colimit of \(X\), if it exists, is called the geometric realization of \(X\), and is denoted by \[ \abs {X} \quad := \quad \colim _{[n] \in \simp \catop } X_n. \] If \(C\) admits all \(\simp \catop \)-indexed colimits, we denote the resulting colimit functor by \(\abs {-}\colon \s C \to C\).