Bourbaki

Corollary 1

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

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

Suppose that X is unlaceable and that the group G is generated by the stabilizers of the points of X. The canonical morphism π1(f,o):π1(X,o)→π1(Y,f(o))\pi_1(f, o):\pi_1(X, o)\rightarrow \pi_1(Y, f(o)) is then surjective. In particular, if X is simply connected by arcs, the same is true of Y.

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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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.