Simplicial and Dendroidal Homotopy Theory

Gijs Heuts, Ieke Moerdijk

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English

Springer International Publishing AG
03 August 2022

Algebra; Algebraic topology

Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

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.

By: Gijs Heuts, Ieke Moerdijk
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2022
Volume: 75
Dimensions: Height: 235mm, Width: 155mm,
Weight: 1.105kg
ISBN: 9783031104466
ISBN 10: 3031104463
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Pages: 612
Publication Date: 03 August 2022
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Reviews for Simplicial and Dendroidal Homotopy Theory

“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)