Kerodon

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Example 5.2.6.10. Let $F: X(0) \rightarrow X(1)$ be a morphism of simplicial sets, which we identify with a diagram $\overrightarrow {X}: [1] \rightarrow \operatorname{Set_{\Delta }}$. Then the mapping simplex $M( \overrightarrow {X} )$ can be identified with the pushout $( \Delta ^1 \times X(0) ) \coprod _{ (\{ 1\} \times X(0))} X(1)$.