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Dualities for modal algebras from the point of view of triples

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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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Authors and Affiliations

  1. Center for Research and Development in Mathematics and Applications, Department of Mathematics, University of Aveiro, 3810-193, Aveiro, Portugal

    Dirk Hofmann & Pedro Nora

Authors
  1. Dirk Hofmann
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  2. Pedro Nora
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Correspondence to Dirk Hofmann.

Additional information

Presented by M. Haviar.

Partial financial assistance by Portuguese funds through CIDMA (Center for Research and Development in Mathematics and Applications), and the Portuguese Foundation for Science and Technology (“FCT – Fundação para a Ciência e a Tecnologia”), within the project PEst-OE/MAT/UI4106/2014, and by the project NASONI under the contract PTDC/EEICTP/ 2341/2012 is gratefully acknowledged.

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Hofmann, D., Nora, P. Dualities for modal algebras from the point of view of triples. Algebra Univers. 73, 297–320 (2015). https://doi.org/10.1007/s00012-015-0324-5

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