Topological Features of Lax Algebras

• Autor(a) principal: Clementino, Maria Manuel
• Data de Publicação: 2003
• Outros Autores: Hofmann, Dirk
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10316/7752; https://doi.org/10.1023/A:1024274315778

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 Cech–Stone compactification of lax algebras.