On Enumerated Algebras and Some Monads in the Category of Enumerated Sets

Article type: Research Article

Authors: Orlicki, Andrzej

Affiliations: University of Toruń

Abstract: In this paper we investigate some properties of categories of enumerated algebras. In section 1 we prove that in case of the category of enumerated algebras satisfying some fixed set of identities, the forgetful functor into the category of enumerated sets is monadic. Then in sections 2 and 3 some applications of this result are presented. In particular, we show (see Theorem 3.2, section 3) that each finitary monad in the category of denumerable sets has a lifting to a monad in the category of enumerated sets.

Keywords: enumerated type of algebras, enumerated algebra, monad, monadic functor, category of enumerated sets

DOI: 10.3233/FI-1985-83-403

Journal: Fundamenta Informaticae, vol. 8, no. 3-4, pp. 285-307, 1985