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?

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