By Adamek J.
An easy, direct facts of the subsequent characterization of sorts of (finitary)algebras is gifted: a cocomplete class is reminiscent of a spread iff it has an algebraic generator, i.e., a customary generator that is precisely projective and finitely generated. This improves a bit of a contemporary 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 proven.
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A categorical characterization of varieties by Adamek J.