Theorem 59.18.8. On $\textit{PAb}(\mathcal{C})$ the functors $\check{H}^ p(\mathcal{U}, -)$ are the right derived functors of $\check{H}^0(\mathcal{U}, -)$.

Proof. By the Lemma 59.18.7, the functors $\check H^ p(\mathcal{U}, -)$ are universal $\delta$-functors since they are effaceable. So are the right derived functors of $\check H^0(\mathcal{U}, -)$. Since they agree in degree $0$, they agree by the universal property of universal $\delta$-functors. For more details see Cohomology on Sites, Lemma 21.9.6. $\square$

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 03OS. Beware of the difference between the letter 'O' and the digit '0'.