Traces and higher structures

Abstract: Quantum topologists are used to thinking about traces in the framework of pivotal tensor categories and thus in a two-dimensional context to which a two-dimensional graphical calculus can be associated. We explain that traces are already naturally defined for twisted endomorphisms of linear categories, i.e. in a one-dimensional context. The endomorphisms are twisted by the Nakayama functor which, for a module category over a monoidal category, is a twisted module functor and hence an inherently three-dimensional object. This naturally leads to a three-dimensional graphical calculus. This calculus also has applications to Turaev–Viro topological field theories with defects.

mathematical physicsalgebraic topologycategory theoryquantum algebra

Audience: researchers in the topic

Topological Quantum Field Theory Club (IST, Lisbon)

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