The Stacks project

Lemma 60.8.2. In Situation 60.7.5. The category $\text{CRIS}(X/S)$ has all finite nonempty limits, in particular products of pairs and fibre products. The functor (60.8.1.1) commutes with limits.

Proof. Omitted. Hint: See Lemma 60.5.3 for the affine case. See also Divided Power Algebra, Remark 23.3.5. $\square$

Comments (0)

There are also:

  • 2 comment(s) on Section 60.8: The big crystalline site

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Your email address will not be published.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 07I9. Beware of the difference between the letter 'O' and the digit '0'.



View Lemma 60.8.2 as pdf