Abstract
In this paper we expand previous results obtained in [2] about the study of categorical equivalence between the category IRL 0 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 \({{\mathsf{K}^\bullet}}\), 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 \({MV^{\bullet}}\) of monadic MV-algebras induced by “Kalman’s functor” \({\mathsf{K}^\bullet}\). Moreover, we extend the construction to ℓ-groups introducing the new category of monadic ℓ-groups together with a functor \({\Gamma ^\sharp}\), that is “parallel” to the well known functor \({\Gamma}\) between ℓ and MV-algebras.
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Castiglioni, J.L., Lewin, R.A. & Sagastume, M. On a Definition of a Variety of Monadic ℓ-Groups. Stud Logica 102, 67–92 (2014). https://doi.org/10.1007/s11225-012-9464-1
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DOI: https://doi.org/10.1007/s11225-012-9464-1