On Some Categories of Involutive Centered Residuated Lattices

Motivated by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras we define the functor K• relating integral residuated lattices with 0 (IRL0) with certain involutive residuated lattices. Our work is also based on the results obtained by Cignoli about...

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Autores principales: Castiglioni, José Luis, Menni, Matías, Sagastume, Marta Susana
Formato: Articulo
Lenguaje:Inglés
Publicado: 2008
Materias:
Matemática
residuated lattices
involution
Kalman functor
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/139459
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-139459
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
residuated lattices
involution
Kalman functor
spellingShingle Matemática
residuated lattices
involution
Kalman functor
Castiglioni, José Luis
Menni, Matías
Sagastume, Marta Susana
On Some Categories of Involutive Centered Residuated Lattices
topic_facet Matemática
residuated lattices
involution
Kalman functor
description Motivated by an old construction due to J. Kalman that relates distributive lattices and centered Kleene algebras we define the functor K• relating integral residuated lattices with 0 (IRL0) with certain involutive residuated lattices. Our work is also based on the results obtained by Cignoli about an adjunction between Heyting and Nelson algebras, which is an enrichment of the basic adjunction between lattices and Kleene algebras. The lifting of the functor to the category of residuated lattices leads us to study other adjunctions and equivalences. For example, we treat the functor C whose domain is cuRL, the category of involutive residuated lattices M whose unit is fixed by the involution and has a Boolean complement c (the underlying set of CM is the set of elements greater or equal than c). If we restrict to the full subcategory NRL of cuRL of those objects that have a nilpotent c, then C is an equivalence. In fact, CM is isomorphic to CeM, and Ce is adjoint to (_), where (_) assigns to an object A of IRL0 the product A × A0 which is an object of NRL.
format Articulo
Articulo
author Castiglioni, José Luis
Menni, Matías
Sagastume, Marta Susana
author_facet Castiglioni, José Luis
Menni, Matías
Sagastume, Marta Susana
author_sort Castiglioni, José Luis
title On Some Categories of Involutive Centered Residuated Lattices
title_short On Some Categories of Involutive Centered Residuated Lattices
title_full On Some Categories of Involutive Centered Residuated Lattices
title_fullStr On Some Categories of Involutive Centered Residuated Lattices
title_full_unstemmed On Some Categories of Involutive Centered Residuated Lattices
title_sort on some categories of involutive centered residuated lattices
publishDate 2008
url http://sedici.unlp.edu.ar/handle/10915/139459
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