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We define a traced pseudomonoid as a pseudomonoid in a monoidal bicategoryequipped with extra structure, giving a new characterisation of Cauchy completetraced monoidal categories as algebraic structures in Prof, the monoidalbicategory of profunctors. This enables reasoning about the trace using thegraphical calculus for monoidal bicategories, which we illustrate in detail. Weapply our techniques to study traced &#8727;-autonomous categories, proving anew equivalence result between the left &#8855;-trace and the right&#8523;-trace, and describing a new condition under which traced&#8727;-autonomous categories become autonomous.

Traced Monoidal Categories as Algebraic Structures in Prof