Example 7.10.2 (00W3)—The Stacks project

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Table of contents
Part 1: Preliminaries
Chapter 7: Sites and Sheaves
Section 7.10: Sheafification
Example 7.10.2 (cite)

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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 January 22, 2018 at 16:29

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

Comment #3166 by Johan on February 02, 2018 at 03:38

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?

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