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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
Published electronically: March 29, 2012
MathSciNet review: 2912459
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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.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.