∗-Autonomous categories of bimodules

Bisets as Categories and Tensor Product of Induced Bimodules

Bisets can be considered as categories. This note uses this point of view to give a simple proof of a Mackey-like formula expressing the tensor product of two induced bimodules. AMS subject classification (2000) : 16D20, 20C20.

Compactification of *-autonomous categories

We study the question when a ∗-autonomous (Mix-)category has a representation as a ∗-autonomous category of a compact one. We prove that necessary and sufficient condition is that weak distributivity maps are monic (or, equivalently epic). For a Mix-category, this condition is, in turn, equivalent to the requirement that Mix-maps be monic (or epic). We call categories satisfying this property t...

Nonsymmetric *-Autonomous Categories

Topological ∗-autonomous categories, revisited

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 obj...

Topological ∗ - Autonomous Categories

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 obj...