Overview
- 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
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 75)
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Table of contents (14 chapters)
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Front Matter
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The Elementary Theory of Simplicial and Dendroidal Sets
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Front Matter
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The Homotopy Theory of Simplicial and Dendroidal Sets
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Front Matter
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The Homotopy Theory of Simplicial and Dendroidal Spaces
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
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
About the authors
Bibliographic Information
Book Title: Simplicial and Dendroidal Homotopy Theory
Authors: Gijs Heuts, Ieke Moerdijk
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-031-10447-3
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s) 2022
Hardcover ISBN: 978-3-031-10446-6Published: 03 August 2022
eBook ISBN: 978-3-031-10447-3Published: 02 August 2022
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: XX, 612
Number of Illustrations: 1 b/w illustrations
Topics: Category Theory, Homological Algebra, Algebraic Topology