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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Traces in monoidal categories
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by Stephan Stolz and Peter Teichner PDF
Trans. Amer. Math. Soc. 364 (2012), 4425-4464 Request permission

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
  • MR Author ID: 167655
  • Peter Teichner
  • Affiliation: Max Planck Institute for Mathematics, PO Box 7280, 53072 Bonn, Germany
  • 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.
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • 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
  • MathSciNet review: 2912459