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Dualities for modal algebras from the point of view of triples

Authors
  • Hofmann, Dirk1
  • Nora, Pedro1
  • 1 University of Aveiro, Center for Research and Development in Mathematics and Applications, Department of Mathematics, Aveiro, 3810-193, Portugal , Aveiro (Portugal)
Type
Published Article
Journal
Algebra universalis
Publisher
Springer Basel
Publication Date
Apr 29, 2015
Volume
73
Issue
3-4
Pages
297–320
Identifiers
DOI: 10.1007/s00012-015-0324-5
Source
Springer Nature
Keywords
License
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Abstract

In this paper, we show how the theory of monads can be used to deduce in a uniform manner several duality theorems involving categories of relations on one side and categories of algebras with homomorphisms preserving only some operations on the other. Furthermore, we investigate the monoidal structure induced by the Cartesian product on the relational side and show that in some cases, the corresponding operation on the algebraic side represents bimorphisms.

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