


Categories of lax algebras: a first approach



Description: 
Following the paper of M.M. Clementino and D. Hofmann [2], and having as starting point Barr's description of topological spaces as lax algebras for the ultrafilter monad [1], I am going to present the categories of lax algebras. They represent a suitable generalization of the relational algebras which allow to describe topological structures as well (it turns out that they have indeed a topological nature). The category of reflexive lax algebras has actually a "better behaviour" than the category of reflexive and transitive lax algebras; in fact, it is a quasitopos [3]. In this talk I show that, contrarily to what happens in particular in the category of topological spaces, in categories of reflexive lax algebras regular epimorphisms are pullbackstable. Also some examples are given. [1] M. Barr, Relational Algebras, Springer Lecture Notes in Math. 137 (1970), 3955. [2] M.M. Clementino and D. Hofmann, Topological features of lax algebras, Applied Categorical Structures 11 (2003), 267286. [3] M.M. Clementino, D. Hofmann and W. Tholen, Exponentiability in categories of lax algebras, Theory and Applications of Categories 11 (2003), 337352.

Date: 
20130522

Start Time: 
15:30 
Speaker: 
Pier Giorgio Basile (PhD student)

Institution: 
PhD program UCUP

Place: 
Sala 2.5

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