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G-sheaves on spaces with a free G-action

It is more or less the same as $G$-equivariant objects in the category of sheaves on $X$ with respect to $G$ acting on this category by endofunctors, but the notion of "$G$-equivariant sheaves" is taken … over by sheaves equivariant with respect to a group scheme or to a continuous action of a topological group. …