Traces in symmetric monoidal categories

Abstract

The purpose of this expository note is to describe duality and trace in a symmetric monoidal category, along with important properties (including naturality and functoriality), and to give as many examples as possible. Among other things, this note is intended as background for the generalizations to the context of bicategories and indexed monoidal categories.

25 pages; v2: final version, to appear in Expositiones Mathematicae

References in corpus (4)

• On the Classification of Topological Field Theories
• Duality and traces for indexed monoidal categories
• Fixed point theory and trace for bicategories
• The multiplicativity of fixed point invariants

Cited by in corpus (6)

• Traces in monoidal derivators, and homotopy colimits
• $K$-theory of endomorphisms, the $TR$-trace, and zeta functions
• The Becker-Gottlieb Transfer Is Functorial
• Coincidence invariants and higher Reidemeister traces
• The Lefschetz-Lunts formula for deformation quantization modules
• Induced monoidal structure from the functor