Iterated traces in 2-categories and Lefschetz theorems

TL;DR

This paper establishes a general theorem on iterated 2-categorical traces, unifying various Lefschetz-type theorems and enabling spectral generalizations within a broad mathematical framework.

Contribution

It introduces a comprehensive theorem on iterated traces in 2-categories, connecting and extending existing Lefschetz theorems with new spectral insights.

Findings

Many Lefschetz theorems are special cases of the main result

The new perspective simplifies proofs of classical theorems

Enables immediate spectral generalizations

Abstract

While not obvious from its initial motivation in linear algebra, there are many context where iterated traces can be defined. In this paper we prove a very general theorem about iterated 2-categorical traces. We show that many Lefschetz-type theorems in the literature are consequences of this result and the new perspective we provide allows for immediate spectral generalizations.