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• W3099385611 abstract "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 bicategory equipped with an extra structure called a “shadow”. In particular, we prove its functoriality and 2-functoriality, which are essential to its applications in fixed-point theory. Throughout we make use of an appropriate “cylindrical” type of string diagram, which we justify formally in an appendix." @default.
• W3099385611 created "2020-11-23" @default.
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• W3099385611 date "2012-10-30" @default.
• W3099385611 modified "2023-10-18" @default.
• W3099385611 title "Shadows and traces in bicategories" @default.
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• W3099385611 doi "https://doi.org/10.1007/s40062-012-0017-0" @default.
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