Abstract
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.
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Clementino, M.M., Hofmann, D. Topological Features of Lax Algebras. Applied Categorical Structures 11, 267–286 (2003). https://doi.org/10.1023/A:1024274315778
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DOI: https://doi.org/10.1023/A:1024274315778