Scholium

Tag 01Z4, permanent. Cite it as [Bourbaki, Tag 01Z4].

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

Let X be an arcwise connected topological space and let $x$ be a point of X. Proposition 6 makes it possible to define a canonical bijection of the set of free homotopy classes of loops in X onto the set of conjugacy classes in $\pi_1(X, x)$ .

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.

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