Split simplicial objects

Definition 21.7.1 ([Lurie (2017), Definition 4.7.2.2]). An augmented simplicial object \(X\colon \simp _+\catop \to C\) is split if it extends to a functor \(\simp _{-\infty }\catop \to C\). A simplicial object is split if it extends to a split augmented simplicial object.

Let \(G\colon D \to C\) be a functor. A simplicial object \(X_\bullet \colon \simp \catop \to D\) is \(G\)-split if \(GX_\bullet \) is split in \(C\).