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?

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  • 8 comment(s) on Section 7.10: Sheafification

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