## “Internal Neighbourhood Spaces: Closed and closed morphisms”

Giovedì 26 Gennaio 2023, ore 15:00 - Aula ABC45 - Partha Ghosh (University of South Africa)

Abstract

The notion of a topological space was internalized within a category with finite limits, finite coproducts, a proper factorization system and good subobjects making a complete lattice as a categorical neighborhood operator. In the present talk I shall exhibit the following notions and discuss some of their properties:

1. closure and closed morphisms,
2. stably closed morphisms, i.e., proper morphisms and hence compact spaces,
3. separated morphisms and hence Hausdorff spaces,
4. perfect morphisms and hence compact Hausdorff spaces.