The Stacks project

Lemma 115.10.1. Assumptions and notation as in Simplicial, Lemma 14.32.1. There exists a section $g : U \to V$ to the morphism $f$ and the composition $g \circ f$ is homotopy equivalent to the identity on $V$. In particular, the morphism $f$ is a homotopy equivalence.

Proof. Immediate from Simplicial, Lemmas 14.32.1 and 14.30.8. $\square$

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