Example 7.5.6.4 (Projectively Cofibrant Sequences). A sequential diagram of simplicial sets
\[ X(0) \rightarrow X(1) \rightarrow X(2) \rightarrow X(3) \rightarrow \cdots \]
is projectively cofibrant (when regarded as a functor $\operatorname{\mathbf{Z}}_{\geq 0} \rightarrow \operatorname{Set_{\Delta }})$ if and only if each of the transition maps $X(n) \rightarrow X(n+1)$ is a monomorphism.