Simplicial and Dendroidal Homotopy Theory

This book provides a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces,which are essential for the study of categories,operads,and algebraic structure up to coherent homotopy. It combines the combinatorics of trees with the theory of Quillen model categories and offers an original account of the more established simplicial approach to infinity-categories.

Format: Hardback
Length: 612 pages
Publication date: 03 August 2022
Publisher: Springer International Publishing AG

This open-access book provides a comprehensive self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces, which are fundamental for the study of categories, operads, and algebraic structure up to coherent homotopy. The dendroidal theory seamlessly blends the combinatorics of trees with the theory of Quillen model categories, offering a natural generalization of simplicial sets from the perspective of operads. Dendroidal sets are a powerful tool for understanding higher operad theory, and this book carefully develops this dendroidal theory. In parallel, the book also presents an original account of the more established simplicial approach to infinity-categories, highlighting the similarities and differences between the two approaches.

Designed with the beginning researcher in mind, this book is an ideal resource for seminars and courses. It can also serve as a standalone introduction to simplicial homotopy theory, the theory of infinity-categories, or the theory of Quillen model categories and Bousfield localization.

The book is carefully written and accessible, making it an invaluable resource for anyone interested in the field of homotopy theory. Its comprehensive coverage and clear explanations make it suitable for both students and researchers alike. Whether you are a seasoned expert or a newcomer to the field, this book will provide you with the foundations you need to advance your understanding of these complex concepts.

Weight: 1105g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031104466
Edition number: 1st ed. 2022