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Simplicial and Dendroidal Homotopy Theory

Ieke Moerdijk author Gijs Heuts author

Format:Hardback

Publisher:Springer International Publishing AG

Published:3rd Aug '22

Currently unavailable, and unfortunately no date known when it will be back

Simplicial and Dendroidal Homotopy Theory cover

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)

ISBN: 9783031104466

Dimensions: unknown

Weight: unknown

612 pages

1st ed. 2022