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Tag 08X8

Chapter 34: Descent > Section 34.4: Descent for universally injective morphisms > Lemma 34.4.20

\begin{equation} \tag{} \xymatrix@C=8pc{ f_*(M, \theta) \otimes_R S \ar[r]^{\theta \circ (1_M \otimes \delta_0^1)} & M \otimes_{S, \delta_1^1} S_2 \ar@<1ex>[r]^{(\theta \otimes \delta_2^2) \circ (1_M \otimes \delta^2_0)} \ar@<-1ex>[r]_{1_{M \otimes S_2} \otimes \delta^2_1} & M \otimes_{S, \delta_{12}^1} S_3 } \end{equation}

    The code snippet corresponding to this tag is a part of the file descent.tex and is located in lines 1210–1220 (see updates for more information).

    f_*(M, \theta) \otimes_R S
    \ar[r]^{\theta \circ (1_M \otimes \delta_0^1)} &
    M \otimes_{S, \delta_1^1} S_2 
    \ar@<1ex>[r]^{(\theta \otimes \delta_2^2) \circ (1_M \otimes \delta^2_0)}
    \ar@<-1ex>[r]_{1_{M \otimes S_2} \otimes \delta^2_1} &
    M \otimes_{S, \delta_{12}^1} S_3

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