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A variety of algebras is nothing else than the category of algebras of a finitary monad on Set, and, in this case, an algebra A is finitely presentable if it can be presented by a finite set of generators and a finite set of equations. We generalize this to finitary regular monads on locally finitely presentable categories. This is based on joint work with J. Adamek, S. Milius and T. Wissmann, recently published as paper 37 in Vol. 34 of the Theory and Applications of Categories.
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