Geodesic
Bicategorical traces and cotraces
Theory and applications of categories, Tome 41 (2024), pp. 707-759 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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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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Classification : 16D90, 18D15, 18M05, 18M30, 18N10
Keywords: bicategory, cotrace, Hochschild homology, Morita equivalence, shadow, string diagram, trace 
@article{TAC_2024_41_a21,
     author = {Justin Barhite},
     title = {Bicategorical traces and cotraces},
     journal = {Theory and applications of categories},
     pages = {707--759},
     year = {2024},
     volume = {41},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2024_41_a21/}
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Justin Barhite. Bicategorical traces and cotraces. Theory and applications of categories, Tome 41 (2024), pp. 707-759. http://geodesic.mathdoc.fr/item/TAC_2024_41_a21/