The Stacks project

Lemma 7.37.1. Let $\mathcal{C}$ be a site. Let $u, u' : \mathcal{C} \to \textit{Sets}$ be two functors, and let $t : u' \to u$ be a transformation of functors. Then we obtain a canonical transformation of stalk functors $t_{stalk} : \mathcal{F}_{p'} \to \mathcal{F}_ p$ which agrees with $t$ via the identifications of Lemma 7.32.3.

Proof. Omitted. $\square$

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View Lemma 7.37.1 as pdf