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.
Keywords: bicategory, cotrace, Hochschild homology, Morita equivalence, shadow, string diagram, trace
2020 MSC: 16D90, 18D15, 18M05, 18M30, 18N10
Theory and Applications of Categories, Vol. 41, 2024, No. 22, pp 707-759.
Published 2024-07-07.
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