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.

There are also:

• 4 comment(s) on Section 35.4: Descent for universally injective morphisms

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar).