Bourbaki

Corollary 1

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

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

Suppose moreover that the spaces X and Y are arcwise connected and let aa be a point of X. The canonical mapping of π1(Y,f(a))\pi_1(Y, f(a)) into π1(\pi_1(Cone(f),f(a))(f), f(a)) is surjective, and its kernel is the smallest normal subgroup which contains the image of the homomorphism π1(f,a)\pi_1(f, a).

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.