Kerodon

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Example 1.1.6.10. Let $I$ be a set and let $\underline{I}_{\bullet }$ be the constant simplicial set associated to $I$ (Construction 1.1.4.2). Then the connected components of $\underline{I}_{\bullet }$ are exactly the simplicial subsets of the form $\{ i \} = \underline{ \{ i \} }_{\bullet }$ for $i \in I$. In particular, we have a canonical bijection $I \simeq \pi _0( \underline{I}_{\bullet } )$.