Bourbaki

Definition 1

Tag 067H, permanent. Cite it as [Bourbaki, Tag 067H].

Algebra, chapter III, § 11. Cogebras, products of multilinear forms, inner products and duality

A cogebr a over A (or A-cogebra, or simply cogebr a if no confusion can arise) is a set E with a structure defined by giving the following: (1) an A-module structure on E; (2) an A-linear mapping c: E → E ⊗_A E called the coproduct of E.

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

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Cites

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Transcribed from the printed edition, 1998, Springer. Not translated.