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.
"Topological $\ast$-autonomous categories, revisited." Tbilisi Math. J. 10 (3) 51 - 64, June 2017. https://doi.org/10.1515/tmj-2017-0102