A Categorical Equivalence Motivated by Kalman’s Construction

An equivalence between the category of MV-algebras and the category (Formula presented.) is given in Castiglioni et al. (Studia Logica 102(1):67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations (Formula presented.) and (Formula presente...

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Detalhes bibliográficos
Autores: Sagastume, Marta Susana, San Martín, Hernán Javier
Tipo de documento: artigo
Estado:Versão publicada
Data de publicação:2016
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositório:CONICET Digital (CONICET)
Idioma:inglês
OAI Identifier:oai:ri.conicet.gov.ar:11336/54338
Acesso em linha:http://hdl.handle.net/11336/54338
Access Level:Acceso aberto
Palavra-chave:Adjunction
Categorical Equivalence
Ideals
Mv-Algebras
https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
Descrição
Resumo:An equivalence between the category of MV-algebras and the category (Formula presented.) is given in Castiglioni et al. (Studia Logica 102(1):67–92, 2014). An integral residuated lattice with bottom is an MV-algebra if and only if it satisfies the equations (Formula presented.) and (Formula presented.). An object of (Formula presented.) is a residuated lattice which in particular satisfies some equations which correspond to the previous equations. In this paper we extend the equivalence to the category whose objects are pairs (A, I), where A is an MV-algebra and I is an ideal of A.