Lemma 14.21.3 (018N)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 14: Simplicial Methods
Section 14.21: Left adjoints to the skeleton functors
Lemma 14.21.3 (cite)

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Lemma 14.21.3. Let $\mathcal{C}$ be a category which has finite colimits. Let $U$ be an $m$ -truncated simplicial object of $\mathcal{C}$ . The map $U \to \text{sk}_ m i_{m!}U$ is an isomorphism.

Proof. Combine Lemmas 14.21.1 and 14.21.2. $\square$

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