# Algebra Seminar talk

2015-05-22

Josef **Šlapal** (Brno University of Technology)*A categorical approach to convergence: compactness*

Abstract:

We will introduce a convergence class on every object of a given category by using certain generalized nets for expressing the convergence. The obtained concrete category will then be studied whose objects are the pairs consisting of objects of the original category and convergence classes on them and whose morphisms are the morphisms of the original category that preserve the convergence. In particular, naturally defined separation and compactness of objects of the concrete category under investigation will be discussed.