Remark 7.14.9 (00X8)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 7: Sites and Sheaves
Section 7.14: Morphisms of sites
Remark 7.14.9 (cite)

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Remark 7.14.9. (Skip on first reading.) Let $\mathcal{C}$ and $\mathcal{D}$ be sites. Analogously to Definition 7.14.1 we say that a quasi-morphism of sites $f : \mathcal{D} \to \mathcal{C}$ is given by a quasi-continuous functor $u : \mathcal{C} \to \mathcal{D}$ (see Remark 7.13.6) such that $u_ s$ is exact. The analogue of Proposition 7.14.7 in this setting is obtained by replacing the word “continuous” by the word “quasi-continuous”, and replacing the word “morphism” by “quasi-morphism”. The proof is literally the same.

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Comment #179 by David Roberts on March 25, 2013 at 01:53

The second sentence, starting "Analogously to Definition 7.14.1..." has a rendering error:

"...a {\it quasi-morphism of sites $f\colon D\to C$ } ..."

Comment #181 by Johan on March 27, 2013 at 18:00

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