A generalization of the notion of trace in a monoidal category to a bicategory context, based on equipping the bicategory with a “shadow” or categorified trace (including the trace of a category).
The following traditional notions of “traces” turn out to be special cases of bicategorical traces
All symmetric monoidal traces, such as the Lefschetz number.
The Reidemeister trace.
A survey is in
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