Lemma 14.31.2 (08NV)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 14: Simplicial Methods
Section 14.31: Kan fibrations
Lemma 14.31.2 (cite)

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Lemma 14.31.2. Let $f : X \to Y$ be a Kan fibration of simplicial sets. Let $Y' \to Y$ be a morphism of simplicial sets. Then $X \times _ Y Y' \to Y'$ is a Kan fibration.

Proof. This follows immediately from the functorial properties of the fibre product (Lemma 14.7.2) and the definitions. $\square$

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