Example 1.2.1.10. Let $I$ be a set and let $\underline{I}_{}$ be the constant simplicial set associated to $I$ (Construction 1.1.5.2). Then the connected components of $\underline{I}_{}$ are exactly the simplicial subsets of the form $\underline{ \{ i \} }$ for $i \in I$. In particular, we have a canonical bijection $I \simeq \pi _0( \underline{I}_{} )$.
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