Applied Categorical Structures

, Volume 11, Issue 3, pp 267–286 | Cite as

Topological Features of Lax Algebras

  • Maria Manuel Clementino
  • Dirk Hofmann


Having as starting point Barr's description of topological spaces as lax algebras for the ultrafilter monad, in this paper we present further topological examples of lax algebras – such as quasi-metric spaces, approach spaces and quasi-uniform spaces – and show that, in a suitable setting, the categories of lax algebras have indeed a topological nature. Furthermore, we generalize to this setting known properties of special categories of lax algebras and, extending the construction of Manes, we describe the Čech–Stone compactification of lax algebras.

(lax) monad (lax) algebra ultrafilter monad topological space approach space quasi-uniform space Čech–Stone compactification 


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Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Maria Manuel Clementino
    • 1
  • Dirk Hofmann
    • 2
  1. 1.Departamento de MatemáticaUniversidade de CoimbraCoimbraPortugal
  2. 2.Departamento de MatemáticaUniversidade de AveiroAveiroPortugal

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