Corollary 2
Tag 01U9, permanent. Cite it as [Bourbaki, Tag 01U9].
Topologie algébrique, chapter II, § 4. Homotopies
Let G be a groupoid, let X be an oriented forest of G, let be the groupoid deduced from G by contraction of the arrows of X. The canonical morphism of G into is a homotopism.
It follows in fact from remark 1 of II, p. 170 and corollary 2 of II, p. 178 that the hypotheses of proposition 1 are satisfied.
Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.
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