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

is an equalizer.

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