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  • Book
  • Open Access
  • © 2022

Simplicial and Dendroidal Homotopy Theory

  • The first book developing the homotopy theory of infinity-operads, with complete and detailed proofs

  • Provides a self-contained introduction to the theory of simplicial sets and infinity-categories

  • An open access, freely downloadable book

  • This book is open access, which means that you have free and unlimited access

Buying options

Hardcover Book USD 59.99
Price excludes VAT (USA)

Table of contents (14 chapters)

  1. Front Matter

    Pages i-xx
  2. The Elementary Theory of Simplicial and Dendroidal Sets

    1. Front Matter

      Pages 1-1
    2. Operads

      • Gijs Heuts, Ieke Moerdijk
      Pages 3-48Open Access
    3. Simplicial Sets

      • Gijs Heuts, Ieke Moerdijk
      Pages 49-90Open Access
    4. Dendroidal Sets

      • Gijs Heuts, Ieke Moerdijk
      Pages 91-131Open Access
    5. Tensor Products of Dendroidal Sets

      • Gijs Heuts, Ieke Moerdijk
      Pages 133-160Open Access
    6. Kan Conditions for Simplicial Sets

      • Gijs Heuts, Ieke Moerdijk
      Pages 161-210Open Access
    7. Kan Conditions for Dendroidal Sets

      • Gijs Heuts, Ieke Moerdijk
      Pages 211-261Open Access
  3. The Homotopy Theory of Simplicial and Dendroidal Sets

    1. Front Matter

      Pages 263-263
    2. Model Categories

      • Gijs Heuts, Ieke Moerdijk
      Pages 265-301Open Access
    3. Model Structures on the Category of Simplicial Sets

      • Gijs Heuts, Ieke Moerdijk
      Pages 303-352Open Access
    4. Three Model Structures on the Category of Dendroidal Sets

      • Gijs Heuts, Ieke Moerdijk
      Pages 353-420Open Access
  4. The Homotopy Theory of Simplicial and Dendroidal Spaces

    1. Front Matter

      Pages 421-421
    2. Reedy Categories and Diagrams of Spaces

      • Gijs Heuts, Ieke Moerdijk
      Pages 423-451Open Access
    3. Mapping Spaces and Bousfield Localizations

      • Gijs Heuts, Ieke Moerdijk
      Pages 453-480Open Access
    4. Dendroidal Spaces and ∞-Operads

      • Gijs Heuts, Ieke Moerdijk
      Pages 481-521Open Access
    5. Left Fibrations and the Covariant Model

      • Gijs Heuts, Ieke Moerdijk
      Pages 523-553Open Access
    6. Simplicial Operads and ∞-Operads

      • Gijs Heuts, Ieke Moerdijk
      Pages 555-590Open Access
  5. Back Matter

    Pages 591-612

About this book

This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. These are essential for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory combines the combinatorics of trees with the theory of Quillen model categories.
 
Dendroidal sets are a natural generalization of simplicial sets from the point of view of operads. In this book, the simplicial approach to higher category theory is generalized to a dendroidal approach to higher operad theory. This dendroidal theory of higher operads is carefully developed in this book. The book also provides an original account of the more established simplicial approach to infinity-categories, which is developed in parallel to the dendroidal theory to emphasize the similarities and differences.
 
Simplicial and Dendroidal Homotopy Theory is a complete introduction, carefully written with the beginning researcher in mind and ideally suited for seminars and courses. It can also be used as a standalone introduction to simplicial homotopy theory and to the theory of infinity-categories, or a standalone introduction to the theory of Quillen model categories and Bousfield localization.

Keywords

  • Open Access
  • Operads
  • infinity-operad
  • infinity-category
  • simplicial set
  • dendroidal set
  • simplicial space
  • simplicial operad
  • model categories
  • Bousfield localization
  • Boardman-Vogt
  • higher algebra

Authors and Affiliations

  • Mathematical Institute, Utrecht University, Utrecht, The Netherlands

    Gijs Heuts, Ieke Moerdijk

About the authors

Both authors are experienced researchers in the field who have contributed significantly to the development of the theory contained in this book. They have lectured extensively on simplicial and dendroidal sets.

Bibliographic Information

Buying options

Hardcover Book USD 59.99
Price excludes VAT (USA)