Definition 1

Tag 05N2, permanent. Cite it as [Bourbaki, Tag 05N2].

An A-module P is called projective if, for every exact sequence F' → F → F'' of A-linear mapping, the sequence

\operatorname{Hom}(P, F') \to \operatorname{Hom}(P, F) \to \operatorname{Hom}(P, F'')

is exact.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.