Kerodon

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Example 5.2.6.6. Let $X$ be a simplicial set, let $n$ be a nonnegative integer, and let $\overrightarrow {X}: [n] \rightarrow \operatorname{Set_{\Delta }}$ denote the constant diagram

\[ X \xrightarrow { \operatorname{id}_ X } X \xrightarrow { \operatorname{id}_ X } X \xrightarrow { \operatorname{id}_ X } \cdots \xrightarrow { \operatorname{id}_ X} X. \]

Then the mapping simplex $M( \overrightarrow {X} )$ can be identified with the cartesian product $\Delta ^ n \times X$.