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Modules over Operads and Functors

  • Benoit Fresse

Part of the Lecture Notes in Mathematics book series (LNM, volume 1967)

Table of contents

  1. Front Matter
    Pages 1-8
  2. Benoit Fresse
    Pages 1-13
  3. Categorical and operadic background

    1. Front Matter
      Pages 17-20
    2. Benoit Fresse
      Pages 21-34
    3. Benoit Fresse
      Pages 1-18
    4. Back Matter
      Pages 95-96
  4. The category of right modules over operads and functors

    1. Front Matter
      Pages 98-98
    2. Benoit Fresse
      Pages 99-106
    3. Benoit Fresse
      Pages 107-112
    4. Benoit Fresse
      Pages 121-128
    5. Benoit Fresse
      Pages 129-138
    6. Benoit Fresse
      Pages 139-147
    7. Back Matter
      Pages 149-149
  5. Homotopical background

    1. Front Matter
      Pages 152-152
    2. Benoit Fresse
      Pages 185-202
    3. Benoit Fresse
      Pages 203-214
    4. Back Matter
      Pages 215-216
  6. The homotopy of modules over operads and functors

    1. Front Matter
      Pages 218-218
    2. Benoit Fresse
      Pages 219-223
    3. Benoit Fresse
      Pages 225-233
    4. Benoit Fresse
      Pages 241-259
    5. Back Matter
      Pages 261-261
  7. Appendix: technical verifications

    1. Front Matter
      Pages 1-2
    2. Benoit Fresse
      Pages 267-276
    3. Benoit Fresse
      Pages 277-286
  8. Back Matter
    Pages 1-23

About this book

Introduction

The notion of an operad supplies both a conceptual and effective device to handle a variety of algebraic structures in various situations. Operads were introduced 40 years ago in algebraic topology in order to model the structure of iterated loop spaces. Since then, operads have been used fruitfully in many fields of mathematics and physics.

This monograph begins with a review of the basis of operad theory. The main purpose is to study structures of modules over operads as a new device to model functors between categories of algebras as effectively as operads model categories of algebras.

Keywords

Algebraic structure Algebraic topology Cohomology Theory Homotopy Model Category Operad Symmetric Monoidal Category homology

Authors and affiliations

  • Benoit Fresse

There are no affiliations available

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-89056-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-89055-3
  • Online ISBN 978-3-540-89056-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site