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Functors between categories of equivariant sheaves are equivariant sheaves on the product?

Let $G$ be a discrete group and $X$ a $G$-set. The equivariant category $X//G$ has elements of $X$ as objects, each triple $(g,x,g\cdot x)$ defines a morphism $x \to g\cdot x$, the composition corresp …
Anton Fetisov's user avatar