The Stacks project

Example 7.10.2. A particular example is the limit over the empty diagram. This gives the final object in the category of (pre)sheaves. It is the presheaf that associates to each object $U$ of $\mathcal{C}$ a singleton set, with unique restriction mappings and moreover this presheaf is a sheaf. We often denote this sheaf by $*$.

Comments (2)

Comment #3062 by William Chen on

The way this is worded, the third sentence might be interpreted as saying that the functor which associates to every object of a singleton set is a sheaf (which is not true)...

Comment #3166 by on

Hi William Chen, thanks very much for your very good comment. I've addressed it here. As you can see I have also added your name to the contributors. Except I wonder if you are the "Will Chen" that was already mentioned there?

There are also:

  • 8 comment(s) on Section 7.10: Sheafification

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Your email address will not be published.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 00W3. Beware of the difference between the letter 'O' and the digit '0'.



View Example 7.10.2 as pdf