Definition 35.4.19 (08X5)—The Stacks project

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Table of contents
Part 2: Schemes
Chapter 35: Descent
Section 35.4: Descent for universally injective morphisms
Definition 35.4.19 (cite)

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Definition 35.4.19. Define the functor $f_*$ $: DD_{S/R} \to \text{Mod}_ R$ by taking $f_*(M, \theta )$ to be the $R$ -submodule of $M$ for which the diagram

35.4.19.1

$\begin{equation} \label{descent-equation-equalizer-f} \xymatrix@C=8pc{f_*(M,\theta ) \ar[r] & M \ar@<1ex>^{\theta \circ (1_ M \otimes \delta _0^1)}[r] \ar@<-1ex>_{1_ M \otimes \delta _1^1}[r] & M \otimes _{S, \delta _1^1} S_2 } \end{equation}$

is an equalizer.

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