Traces in monoidal categories

Authors:
Stephan Stolz and Peter Teichner

Journal:
Trans. Amer. Math. Soc. **364** (2012), 4425-4464

MSC (2010):
Primary 18D10; Secondary 46A32, 81T99

DOI:
https://doi.org/10.1090/S0002-9947-2012-05615-7

Published electronically:
March 29, 2012

MathSciNet review:
2912459

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Abstract | References | Similar Articles | Additional Information

Abstract: 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.

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Additional Information

**Stephan Stolz**

Affiliation:
Department of Mathematics, University of Notre Dame, South Bend, Indiana 46556

**Peter Teichner**

Affiliation:
Max Planck Institute for Mathematics, PO Box 7280, 53072 Bonn, Germany

DOI:
https://doi.org/10.1090/S0002-9947-2012-05615-7

Received by editor(s):
October 21, 2010

Received by editor(s) in revised form:
April 29, 2011

Published electronically:
March 29, 2012

Additional Notes:
Both authors were partially supported by NSF grants. They would like to thank the referee for many valuable suggestions. The first author visited the second author at the Max-Planck-Institut in Bonn during the Fall of 2009 and in July 2010. He would like to thank the institute for its support and for its stimulating atmosphere.

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© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.