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arXiv · 2307.13070

Bicategorical Traces and Cotraces

Justin Barhite
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Abstract

The familiar trace of a square matrix generalizes to a trace of an endomorphism of a dualizable object in a symmetric monoidal category. To extend these ideas to other settings, such as modules over non-commutative rings, the trace can be generalized to a bicategory equipped with additional structure called a shadow. We propose a notion of bicategorical cotrace of certain maps involving dualizable objects in a closed bicategory equipped with a coshadow, and we use this framework to draw connections to work of Lipman on residues and traces with Hochschild (co)homology, and to work of Ganter and Kapranov on 2-representations and 2-characters.

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Justin Barhite. 2023-07-24. Bicategorical Traces and Cotraces. https://arxiv.org/abs/2307.13070

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