The Stacks project

Lemma 7.15.2. Given a morphism of sites $f : \mathcal{D} \to \mathcal{C}$ corresponding to the functor $u : \mathcal{C} \to \mathcal{D}$ the pair of functors $(f^{-1} = u_ s, f_* = u^ s)$ is a morphism of topoi.

Proof. This is obvious from Definition 7.14.1. $\square$

Comments (2)

Comment #10896 by Oliver on

Just a suggestion: I think it would be useful to say here explicitly that the direction of the induced morphism of topoi is from (in particular the morphism of sites and topoi are in the same direction). I often forget and have to retrace the definitions each time - it would be nice to have it explicitly written down somewhere.

Comment #10973 by Alejandro González Nevado on

SS: A morphism of sites canonically induces a morphism of topoi.

There are also:

  • 5 comment(s) on Section 7.15: Topoi

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Your email address will not be published.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



View Lemma 7.15.2 as pdf