Corollary

Tag 03HT, permanent. Cite it as [Bourbaki, Tag 03HT].

Theory of Sets, chapter II, § 3. Correspondences

Let A, B be sets, let $f$ be a mapping of A into B, and let $g$ be a mapping of B into A. If $g \circ f$ is the identity mapping of A and if $f \circ g$ is the identity mapping of B, then $f$ and $g$ are bijective, and $g = \overset{-1}{f}$ .

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

Remark, § 2

Cites

Nothing.