[2112.14051] Traced Monoidal Categories as Algebraic Structures in Prof
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Mathematics > Category Theory

arXiv:2112.14051 (math)
[Submitted on 28 Dec 2021]

Title:Traced Monoidal Categories as Algebraic Structures in Prof

Authors:Nick Hu (University of Oxford), Jamie Vicary (University of Cambridge)
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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.
Comments: In Proceedings MFPS 2021, arXiv:2112.13746. Please see arXiv:2109.00589 for the extended version of this paper
Subjects: Category Theory (math.CT)
Cite as: arXiv:2112.14051 [math.CT]
  (or arXiv:2112.14051v1 [math.CT] for this version)
  https://doi.org/10.48550/arXiv.2112.14051
Journal reference: EPTCS 351, 2021, pp. 84-97
Related DOI: https://doi.org/10.4204/EPTCS.351.6

Submission history

From: EPTCS [view email] [via EPTCS proxy]
[v1] Tue, 28 Dec 2021 09:07:32 UTC (64 KB)
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