For finitary regular monads T on locally finitely presentable categories we characterize the finitely presentable objects in the category of T-algebras in the style known from general algebra: they are precisely the algebras presentable by finitely many generators and finitely many relations.
Keywords: Finitely presentable object, finitely generated object, finitary functor, regular monad
2010 MSC: 18C35, 18C20, 08C05
Theory and Applications of Categories, Vol. 34, 2019, No. 37, pp 1179-1195.