Lemma 1

Tag 0A1V, permanent. Cite it as [Bourbaki, Tag 0A1V].

Lie Groups and Lie Algebras, chapter II, § 1. Enveloping bigebra of a Lie algebra

Let $\pi : E \to E'$ be a surjective cogebras morphism. If $E$ is coassociative (resp. cocommutative), so is $E'$ .

Let $B$ be an associative $K$ -algebra; the mapping $f \mapsto f \circ \pi$ is an injective algebra homomorphism of $\mathrm{Hom}_K(E', B)$ into $\mathrm{Hom}_K(E, B)$ . It then suffices to apply Proposition 1 (resp. Proposition 2) of Algebra, Chapter III, § 11, no. 2.

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

Cited by

Nothing.

Cites

*Algebra*, Chapter III, § 11, no. 2
Proposition 1
Proposition 2