Lemma 15.89.12 (05EM)—The Stacks project

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Part 1: Preliminaries
Chapter 15: More on Algebra
Section 15.89: Formal glueing of module categories
Lemma 15.89.12 (cite)

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Lemma 15.89.12. Assume $\varphi : R \to S$ is a flat ring map and $I = (f_1, \ldots , f_ t) \subset R$ is an ideal such that $R/I \to S/IS$ is an isomorphism. Then the functor $H^0$ is a left quasi-inverse to the functor $\text{Can}$ of Remark 15.89.10.

Proof. This is a reformulation of Lemma 15.89.9. $\square$

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