On a Definition of a Variety of Monadic l-Groups

J.L. CASTIGLIONI; R. LEWIN; M. SAGASTUME

STUDIA LOGICA

Springer

Año: 2014 vol. 102 p. 67 - 92

0039-3215

In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL0 of integral residuated lattices with bottom, which generalize MV -algebras and a category whose objects are called c-differential residuated lattices. The equivalence is given by a functor K?, motivated by an old construction due to J. Kalman, which was studied by Cignoli in [3] in the context of Heyting and Nelson algebras. These results are then specialized to the case of MV -algebras and the corresponding category MV? of monadic MV -algebras induced by ?Kalman?s functor? K?. Moreover, we extend the construction to l-groups introducing the new category of monadic l-groups together with a functor Ã#, that is ?parallel? to the well known functor à between l-groups and MV -algebras.