Lemma 4.42.4 (02Y8)—The Stacks project

Loading web-font TeX/Caligraphic/Regular

Table of contents
Part 1: Preliminaries
Chapter 4: Categories
Section 4.42: Representable 1-morphisms
Lemma 4.42.4 (cite)

previous definition
next lemma

numberstags

history
statistics

Lemma 4.42.4. Let $\mathcal{C}$ be a category. Let $\mathcal{X}$ , $\mathcal{Y}$ be categories fibred in groupoids over $\mathcal{C}$ . Let $F : \mathcal{X} \to \mathcal{Y}$ be a $1$ -morphism. If $F$ is representable then every one of the functors

$F_ U : \mathcal{X}_ U \longrightarrow \mathcal{Y}_ U$

between fibre categories is faithful.

Proof. Clear from the description of fibre categories in Lemma 4.42.1 and the characterization of representable fibred categories in Lemma 4.40.2. $\square$

Comments (0)

There are also:

1 comment(s) on Section 4.42: Representable 1-morphisms

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