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

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.