Lemma 73.4.12 (0DF7)—The Stacks project

Processing math: 100%

Table of contents
Part 4: Algebraic Spaces
Chapter 73: Topologies on Algebraic Spaces
Section 73.4: Étale topology
Lemma 73.4.12 (cite)

previous lemma
next lemma

numberstags

history
statistics

Lemma 73.4.12. Let $S$ be a scheme. Given morphisms $f : X \to Y$ , $g : Y \to Z$ in $(\textit{Spaces}/S)_{\acute{e}tale}$ we have $g_{big} \circ f_{big} = (g \circ f)_{big}$ and $g_{small} \circ f_{small} = (g \circ f)_{small}$ .

Proof. This follows from the simple description of pushforward and pullback for the functors on the big sites from Lemma 73.4.10. For the functors on the small sites this follows from the description of the pushforward functors in Lemma 73.4.11. $\square$

Comments (0)

There are also:

1 comment(s) on Section 73.4: Étale topology

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$ ). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).

Comments (0)

Post a comment