Topological *-autonomous categories, revisited

TL;DR

This paper explores conditions under which categories of topological objects over an additive equational category with a dualizing object are equivalent to Chu categories, enhancing understanding of topological *-autonomous categories.

Contribution

It establishes sufficient conditions for the category of topological objects to be equivalent to Chu categories, providing a new perspective on topological *-autonomous categories.

Findings

Categories of topological objects can be equivalent to Chu categories under certain conditions.

Full subcategories of strong and weakly topologized objects are well-behaved.

The results unify topological and categorical structures in a novel way.

Abstract

Given an additive equational category with a closed symmetric monoidal structure and a potential dualizing object, we find sufficient conditions that the category of topological objects over that category has a good notion of full subcategories of strong and weakly topologized objects and show that each is equivalent to the chu category of the original category with respect to the dualizing object.