The Stacks project

Lemma 7.19.1. There is a canonical map ${}_ pu\mathcal{F}(u(U)) \to \mathcal{F}(U)$, which is compatible with restriction maps.

Proof. This is just the projection map $c(\text{id}_{u(U)})$ above. $\square$

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View Lemma 7.19.1 as pdf