A Categorical Equivalence Motivated by Kalman’s Construction
An equivalence between the category of MV-algebras and the category MV∙ 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 a=¬¬a,(a→b)∨(b→a)=1 and a⊙(a→b)=a∧b. An object of MV∙ is a...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2015 |
| País: | Argentina |
| Institución: | Universidad Nacional de La Plata |
| Repositorio: | SEDICI (UNLP) |
| Idioma: | inglés |
| OAI Identifier: | oai:sedici.unlp.edu.ar:10915/107887 |
| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/107887 |
| Access Level: | acceso abierto |
| Palabra clave: | Matemática MV-algebras Ideals Adjunction Categorical equivalence |
| Sumario: | An equivalence between the category of MV-algebras and the category MV∙ 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 a=¬¬a,(a→b)∨(b→a)=1 and a⊙(a→b)=a∧b. An object of MV∙ 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. |
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