# Shadows and traces in bicategories

@article{Ponto2009ShadowsAT, title={Shadows and traces in bicategories}, author={Kate Ponto and Michael Shulman}, journal={Journal of Homotopy and Related Structures}, year={2009}, volume={8}, pages={151-200} }

Traces in symmetric monoidal categories are well-known and have many applications; for instance, their functoriality directly implies the Lefschetz fixed point theorem. However, for some applications, such as generalizations of the Lefschetz theorem, one needs “noncommutative” traces, such as the Hattori-Stallings trace for modules over noncommutative rings. In this paper we study a generalization of the symmetric monoidal trace which applies to noncommutative situations; its context is a…

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