The Stacks project

Lemma 14.11.3. Let $U$ be a simplicial set. Let $n \geq 0$ be an integer. There is a canonical bijection

\[ \mathop{\mathrm{Mor}}\nolimits (\Delta [n], U) \longrightarrow U_ n \]

which maps a morphism $\varphi $ to the value of $\varphi $ on the unique nondegenerate $n$-simplex of $\Delta [n]$.

Proof. Omitted. $\square$

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