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Operads Revisited

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Book cover Algebra, Arithmetic, and Geometry

Part of the book series: Progress in Mathematics ((PM,volume 269))

Summary

Operads may be represented as symmetric monoidal functors on a small symmetric monoidal category. We discuss the axioms which must be imposed on a symmetric monoidal functor in order that it give rise to a theory similar to the theory of operads: we call such functors patterns. We also develop the enriched version of the theory, and show how it may be applied to axiomatize topological field theory.

2000 Mathematics Subject Classifications: 18D50, 57R56; 18D10, 18D20, 18C35

To Yuri Manin, many happy returns

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Acknowledgements

I thank Michael Batanin, André Henriques and Steve Lack for very helpful feedback on earlier drafts of this paper.

I am grateful to a number of institutions for hosting me during the writing of this paper: RIMS, University of Nice, and KITP. I am grateful to my hosts at all of these institutions, Kyoji Saito and Kentaro Hori at RIMS, André Hirschowitz and Carlos Simpson in Nice, and David Gross at KITP, for their hospitality.

I am also grateful to Jean-Louis Loday for the opportunity to lecture on an earlier version of this work at Luminy. I received support from NSF Grants DMS-0072508 and DMS-0505669.

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Authors and Affiliations

  1. Northwestern University, Evanston, Illinois, USA

    Ezra Getzler

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  1. Ezra Getzler
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Correspondence to Ezra Getzler .

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Editors and Affiliations

  1. Department of Mathematics, Courant Institute of Math. Sciences, New York University, Mercer St. 251, New York, 10012, New York, USA

    Yuri Tschinkel

  2. Eberly College of Science, Dept. Mathematics, Pennsylvania State University, University Park, 16802, Pennsylvania, USA

    Yuri Zarhin

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Getzler, E. (2009). Operads Revisited. In: Tschinkel, Y., Zarhin, Y. (eds) Algebra, Arithmetic, and Geometry. Progress in Mathematics, vol 269. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4745-2_16

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