Bourbaki

Corollary 3

Tag 023N, permanent. Cite it as [Bourbaki, Tag 023N].

Topologie algébrique, chapter IV, § 5. Théorème de van Kampen

Suppose that X is simply connected by arcs. The mapping of G into π1(Y,f(o))\pi_1(Y, f(o)) which, to g∈g\in G, associates the path class f∗(βg)f_*(\beta_g) is a surjective group homomorphism; its kernel is the subgroup of G generated by the stabilizers of the points of X.

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.

Cited by

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Cites

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Machine translation of the English, by gpt-5-6-mini, gpt-5-6, gpt-5.4, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.