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Operads and Cosimplicial Objects: An Introduction

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Axiomatic, Enriched and Motivic Homotopy Theory

Part of the book series: NATO Science Series ((NAII,volume 131))

Abstract

This paper is an introduction to the series of papers [26, 28, 29, 30], in which we develop a combinatorial theory of certain important operads and their actions.1 The operads we consider are A ∞ operads, E ∞ operads, the little n-cubes operad and the framed little disks operad. Sections 2, 6 and 9, which can be read independently, are an introduction to the theory of operads.

Partially supported by NSF. This paper is based in part on lectures given by the first author at the Newton Institute.

Parially supported by NSF.

The relation between these papers and [27] is explained in Remarks 12.5 and 15.5.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 150 N. University Street, West Lafayette, IN, 47907-2067, USA

    James E. McClure & Jeffrey H. Smith

Authors
  1. James E. McClure
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  2. Jeffrey H. Smith
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  1. University of Sheffield, UK

    J. P. C. Greenlees

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McClure, J.E., Smith, J.H. (2004). Operads and Cosimplicial Objects: An Introduction. In: Greenlees, J.P.C. (eds) Axiomatic, Enriched and Motivic Homotopy Theory. NATO Science Series, vol 131. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-0948-5_5

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  • DOI: https://doi.org/10.1007/978-94-007-0948-5_5

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-1-4020-1834-3

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