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Topological \(\ast\)-autonomous categories. (English) Zbl 1123.18006

Summary: 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.

MSC:

18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
22D35 Duality theorems for locally compact groups
46A20 Duality theory for topological vector spaces
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