Algebra universalis

, Volume 73, Issue 3–4, pp 297–320 | Cite as

Dualities for modal algebras from the point of view of triples

  • Dirk HofmannEmail author
  • Pedro Nora


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.

2010 Mathematics Subject Classification

Primary: 18C15 Secondary: 03G05 03G10 18A40 18C20 54H10 

Key words and phrases

Boolean algebra distributive lattice monad Kleisli construction dual equivalence Stone space spectral space Vietoris functor tensor product 


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© Springer Basel 2015

Authors and Affiliations

  1. 1.Center for Research and Development in Mathematics and Applications, Department of MathematicsUniversity of AveiroAveiroPortugal

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