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

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

Comment #5701 by on

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

There are also:

• 2 comment(s) on Section 7.6: Sites

## Post a comment

Your email address will not be published. Required fields are marked.

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).

Unfortunately JavaScript is disabled in your browser, so the comment preview function will not work.

All contributions are licensed under the GNU Free Documentation License.

In order to prevent bots from posting comments, we would like you to prove that you are human. You can do this by filling in the name of the current tag in the following input field. As a reminder, this is tag 07GE. Beware of the difference between the letter 'O' and the digit '0'.