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.
$\square$

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## Comments (2)

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