Lemma 94.10.3 (045A)—The Stacks project

Loading web-font TeX/Math/Italic

Table of contents
Part 7: Algebraic Stacks
Chapter 94: Algebraic Stacks
Section 94.10: Properties of morphisms representable by algebraic spaces
Lemma 94.10.3 (cite)

previous lemma
next lemma

numberstags

history
statistics
4 tags refer to this tag

Lemma 94.10.3. Let $S$ be a scheme contained in $\mathit{Sch}_{fppf}$ . Let $a : F \to G$ be a map of presheaves on $(\mathit{Sch}/S)_{fppf}$ . Let $\mathcal{P}$ be as in Definition 94.10.1. Assume $a$ is representable by algebraic spaces. Then $a : F \to G$ has property $\mathcal{P}$ (see Bootstrap, Definition 80.4.1) if and only if the corresponding morphism $\mathcal{S}_ F \to \mathcal{S}_ G$ of categories fibred in groupoids has property $\mathcal{P}$ .

Proof. Note that the lemma makes sense by Lemma 94.9.5. Proof omitted. $\square$

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