Traced Monoidal Categories as Algebraic Structures in Prof
Abstract
We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategory equipped with extra structure, giving a new characterisation of Cauchy complete traced monoidal categories as algebraic structures in Prof, the monoidal bicategory of profunctors. This enables reasoning about the trace using the graphical calculus for monoidal bicategories, which we illustrate in detail. We apply our techniques to study traced ∗-autonomous categories, proving a new equivalence result between the left ⊗-trace and the right ⅋-trace, and describing a new condition under which traced ∗-autonomous categories become autonomous.
Cite
@article{arxiv.2112.14051,
title = {Traced Monoidal Categories as Algebraic Structures in Prof},
author = {Nick Hu and Jamie Vicary},
journal= {arXiv preprint arXiv:2112.14051},
year = {2021}
}
Comments
In Proceedings MFPS 2021, arXiv:2112.13746. Please see arXiv:2109.00589 for the extended version of this paper