Lemma 98.13.4 (07XU)—The Stacks project

Processing math: 100%

Table of contents
Part 7: Algebraic Stacks
Chapter 98: Artin's Axioms
Section 98.13: Openness of versality
Lemma 98.13.4 (cite)

previous lemma
next lemma

numberstags

history
statistics
1 tag refers to this tag

Lemma 98.13.4. Let $S$ be a locally Noetherian scheme. Let $f : \mathcal{X} \to \mathcal{Y}$ and $g : \mathcal{Y} \to \mathcal{Z}$ be composable $1$ -morphisms of categories fibred in groupoids over $(\mathit{Sch}/S)_{fppf}$ . If $f$ and $g$ satisfy (98.13.2.1) so does $g \circ f$ .

Proof. This follows formally from Formal Deformation Theory, Lemma 90.8.7. $\square$

Comments (0)

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