Topological features of lax algebras
Abstract: Having as starting point Barr's description of topological spaces
as lax algebras for the ultrafilter monad [2], 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
[11], we describe the Cech-Stone compactification of lax
algebras.
