The Stacks project

Lemma 77.10.2. Let $B \to S$ as in Section 77.3. Let $G$ be a group algebraic space over $B$. Let $f : X \to Y$ be a $G$-equivariant morphism between algebraic spaces over $B$ endowed with $G$-actions. Then pullback $f^*$ given by $(\mathcal{F}, \alpha ) \mapsto (f^*\mathcal{F}, (1_ G \times f)^*\alpha )$ defines a functor from the category of quasi-coherent $G$-equivariant sheaves on $Y$ to the category of quasi-coherent $G$-equivariant sheaves on $X$.

Proof. Omitted. $\square$


Comments (2)

Comment #6697 by on

Looks like and interchanged roles during the course of the statement! And maybe the source category wants to be quasi-coherent as well?


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Your email address will not be published.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 043U. Beware of the difference between the letter 'O' and the digit '0'.