Example 7.6.6 (07GE)—The Stacks project

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Example 7.6.6. Let $\mathcal{C}$ be a category. There is a canonical way to turn this into a site where $\{ f : V \to U \mid f\text{ is an isomorphism}\}$ are the coverings of $U$ . Sheaves on this site are the presheaves on $\mathcal{C}$ . This corresponding topology is called the chaotic or indiscrete topology.

Comments (2)

Comment #5500 by Tim Holzschuh on September 11, 2020 at 03:08

I think one needs to choose all sets of isomorphisms $V \to U$ as coverings, right?

Comment #5701 by Johan on November 15, 2020 at 18:48

OMG, thanks very much! This is yet another mistake I made early on with the material on sites. The change is here.

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