Remark 35.4.21 (08X9)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 35: Descent
Section 35.4: Descent for universally injective morphisms
Remark 35.4.21 (cite)

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Remark 35.4.21. If $f$ is a split injection in $\text{Mod}_ R$ , one can simplify the argument by splitting $f$ directly, without using $C$ . Things are even simpler if $f$ is faithfully flat; in this case, the conclusion of Lemma 35.4.20 is immediate because tensoring over $R$ with $S$ preserves all equalizers.

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