Lemma 8.9.3 (04Y2)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 8: Stacks
Section 8.9: Stackification of categories fibred in groupoids
Lemma 8.9.3 (cite)

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Lemma 8.9.3. Let $\mathcal{C}$ be a site. Let $f : \mathcal{X} \to \mathcal{Y}$ and $g : \mathcal{Z} \to \mathcal{Y}$ be morphisms of categories fibred in groupoids over $\mathcal{C}$ . In this case the stackification of the $2$ -fibre product is the $2$ -fibre product of the stackifications.

Proof. This is a special case of Lemma 8.8.4. $\square$

Comments (4)

Comment #2067 by Matthew Emerton on June 16, 2016 at 10:44

The word ``of'' is missing from the end of the first line of the statement of the lemma.

Comment #2095 by Johan on June 16, 2016 at 15:26

Thanks, fixed here.

Comment #3215 by William Chen on March 07, 2018 at 00:10

Surely g should go from Z to Y, not Y to Z?

Comment #3317 by Johan on May 17, 2018 at 17:34

Thanks, fixed here.

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