Corollary

Tag 01YZ, permanent. Cite it as [Bourbaki, Tag 01YZ].

Topologie algébrique, chapter III, § 3. Groupoïde de Poincaré

Let $a$ be a point of X and let J be the set of $i\in I$ such that $a\in A_i$ . The canonical homomorphism

lim $\longrightarrow_{i\in J}\pi_1(A_i, a)\rightarrow \pi_1(X, a)$

is bijective.

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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