## Traced Monoidal Categories as Algebraic Structures in Prof

 Nick Hu (University of Oxford) Jamie Vicary (University of Cambridge)

 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.

In Ana Sokolova: Proceedings 37th Conference on Mathematical Foundations of Programming Semantics (MFPS 2021), Hybrid: Salzburg, Austria and Online, 30th August - 2nd September, 2021, Electronic Proceedings in Theoretical Computer Science 351, pp. 84–97.
Please see https://arxiv.org/abs/2109.00589 for the extended version of this paper.
Published: 29th December 2021.

 ArXived at: http://dx.doi.org/10.4204/EPTCS.351.6 bibtex PDF

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