Remark 14.21.6. In some texts the composite functor
\text{Simp}(\mathcal{C}) \xrightarrow {\text{sk}_ m} \text{Simp}_ m(\mathcal{C}) \xrightarrow {i_{m!}} \text{Simp}(\mathcal{C})
is denoted \text{sk}_ m. This makes sense for simplicial sets, because then Lemma 14.21.5 says that i_{m!} \text{sk}_ m V is just the sub simplicial set of V consisting of all i-simplices of V, i \leq m and their degeneracies. In those texts it is also customary to denote the composition
\text{Simp}(\mathcal{C}) \xrightarrow {\text{sk}_ m} \text{Simp}_ m(\mathcal{C}) \xrightarrow {\text{cosk}_ m} \text{Simp}(\mathcal{C})
by \text{cosk}_ m.
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