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Traces in monoidal categories. (English) Zbl 1278.18012

Summary: This paper contains the construction, examples and properties of a trace and a trace pairing for certain morphisms in a monoidal category with switching isomorphisms. Our construction of the categorical trace is a common generalization of the trace for endomorphisms of dualizable objects in a balanced monoidal category and the trace of nuclear operators on a topological vector space with the approximation property. In a forthcoming paper, applications to the partition function of super-symmetric field theories will be given.

MSC:

18D10 Monoidal, symmetric monoidal and braided categories (MSC2010)
46A32 Spaces of linear operators; topological tensor products; approximation properties
81T99 Quantum field theory; related classical field theories
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