By Adamek J.

An easy, direct facts of the next characterization of types of (finitary)algebras is gifted: a cocomplete classification is similar to a spread iff it has an algebraic generator, i.e., a customary generator that's precisely projective and finitely generated. This improves a bit a up to date restatement, as a result of Pedicchio and wooden, of the classical characterization theorem of Lawvere. A bijective correspondence among algebraic theories and algebraic turbines is tested.

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