Infinity Properads and Infinity Wheeled Properads

  • Philip Hackney
  • Marcy Robertson
  • Donald Yau

Part of the Lecture Notes in Mathematics book series (LNM, volume 2147)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Philip Hackney, Marcy Robertson, Donald Yau
    Pages 1-10
  3. Infinity Properads

    1. Front Matter
      Pages 11-11
    2. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 13-54
    3. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 55-67
    4. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 69-98
    5. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 99-124
    6. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 125-164
    7. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 165-207
    8. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 209-248
  4. Infinity Wheeled Properads

    1. Front Matter
      Pages 249-249
    2. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 251-291
    3. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 293-339
    4. Philip Hackney, Marcy Robertson, Donald Yau
      Pages 341-345
  5. Back Matter
    Pages 347-360

About this book

Introduction

The topic of this book sits at the interface of the theory of higher categories (in the guise of (∞,1)-categories) and the theory of properads. Properads are devices more general than operads, and enable one to encode bialgebraic, rather than just (co)algebraic, structures.
 
The text extends both the Joyal-Lurie approach to higher categories and the Cisinski-Moerdijk-Weiss approach to higher operads, and provides a foundation for a broad study of the homotopy theory of properads. This work also serves as a complete guide to the generalised graphs which are pervasive in the study of operads and properads. A preliminary list of potential applications and extensions comprises the final chapter.
 
Infinity Properads and Infinity Wheeled Properads is written for mathematicians in the fields of topology, algebra, category theory, and related areas. It is written roughly at the second year graduate level, and assumes a basic knowledge of category theory.

Keywords

Fundamental Properad Graphical Sets Infinity-Properads Infinity-Wheeled Properads Properadic Nerve Properadic Segal Map Properads Symmetric Monoidal Categories Wheeled Properads

Authors and affiliations

  • Philip Hackney
    • 1
  • Marcy Robertson
    • 2
  • Donald Yau
    • 3
  1. 1.Stockholm UniversityStockholmSweden
  2. 2.University of CaliforniaLos AngelesUSA
  3. 3.Ohio State University, Newark CampusNewarkUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-20547-2
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-20546-5
  • Online ISBN 978-3-319-20547-2
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book