Corollary 1

Tag 00AY, permanent. Cite it as [Bourbaki, Tag 00AY].

Algebra, VIII, p. 162, § 9. Radical

Let M be an A-module. Let $(P, u)$ and $(P', u')$ be projective covers of M. There exists an isomorphism $f$ from P to $P'$ such that $u=u'\circ f$ .

Note that $f$ is not necessarily uniquely determined by the relation $u=u'\circ f$ (VIII, p. 170, Exercise 21).

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

Corollary, § 9

Cites

VIII, p. 170, Exercise 21