Lemma 115.10.3. Let $\mathcal{C}$ be a category. Let $X$ be an object of $\mathcal{C}$ such that the self products $X \times \ldots \times X$ exist. Let $k \geq 0$ and let $C[k]$ be as in Simplicial, Example 14.5.6. With notation as in Simplicial, Lemma 14.15.2 the canonical map

is identified with the map

which is the projection onto the factors where $\alpha $ is a constant map.

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