The Stacks project

Lemma 96.19.3. If there exists a $1$-morphism $s : \mathcal{X} \to \mathcal{U}$ such that $f \circ s$ is $2$-isomorphic to $\text{id}_\mathcal {X}$ then the extended relative Čech complex is homotopic to zero.

Proof. Literally the same as the proof of Lemma 96.18.2. $\square$

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View Lemma 96.19.3 as pdf