The Stacks project

Definition 7.29.2. Let $\mathcal{C}$, $\mathcal{D}$ be sites. A special cocontinuous functor $u$ from $\mathcal{C}$ to $\mathcal{D}$ is a cocontinuous functor $u : \mathcal{C} \to \mathcal{D}$ satisfying the assumptions and conclusions of Lemma 7.29.1.


Comments (2)

Comment #2041 by Ruian Chen on

Just out of curiosity, why do we emphasize cocontinuous in the name, as the functor is both cocontinuous and continuous by the assumptions of Lemma 7.28.1 anyway?

Comment #2079 by on

Just a choice and not a very good one. The idea is that these types of functors are easy to study and easy to construct as the material in this section shows. Then we'll use them later to massage any morphism of topoi into a sequence of morphisms of topoi given by these ones or their inverses and morphisms of topoi coming from morphisms of sites. Anyway, can anybody suggest a better terminology?

There are also:

  • 7 comment(s) on Section 7.29: Morphisms of 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Your email address will not be published.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 03CG. Beware of the difference between the letter 'O' and the digit '0'.