Skip to main content

Simplicial and Dendroidal Homotopy Theory

  • Book
  • Open Access
  • © 2022

You have full access to this open access Book


  • The first book developing the homotopy theory of infinity-operads
  • Provides a self-contained introduction to the theory of simplicial sets and infinity-categories
  • Includes complete proofs of all the basic results, with special attention paid to the underlying combinatorics
  • This book is open access, which means that you have free and unlimited access

Buy print copy

Hardcover Book USD 29.99 USD 59.99
50% discount Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Table of contents (14 chapters)

  1. The Elementary Theory of Simplicial and Dendroidal Sets

  2. The Homotopy Theory of Simplicial and Dendroidal Sets

  3. The Homotopy Theory of Simplicial and Dendroidal Spaces


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.


“This book is a readable and carefully organized account of dendroidal sets by two of the main figures in the field. It gives a self-contained, detailed description of dendroidal
sets and spaces … . Each chapter is also accompanied by a short section of historical notes giving background, references, and historical perspectives on the ideas presented.” (Ben C Walter, Mathematical Reviews, December, 2023)

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

Publish with us