Lemma 35.4.18. The diagram

35.4.18.1
$$\label{descent-equation-equalizer-S} \xymatrix@C=8pc{ S_1 \ar[r]^{\delta ^1_1} & S_2 \ar@<1ex>[r]^{\delta ^2_2} \ar@<-1ex>[r]_{\delta ^2_1} & S_3 }$$

is a split equalizer.

Proof. In Lemma 35.4.16, take $(M, \theta ) = f^*(S)$. $\square$

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