Simplicial and Dendroidal Homotopy Theory

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.

“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 dendroidalsets 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)

• Part I The Elementary Theory of Simplicial and Dendroidal Sets.- 1 Operads.- 2 Simplicial Sets.- 3 Dendroidal Sets.- 4 Tensor Products of Dendroidal Sets.- 5 Kan Conditions for Simplicial Sets.- 6 Kan Conditions for Dendroidal Sets.-  Part II The Homotopy Theory of Simplicial and Dendroidal Sets.- 7 Model Categories.- 8 Model Structures on the Category of Simplicial Sets.- 9 Three Model Structures on the Category of Dendroidal Sets.- Part III The Homotopy Theory of Simplicial and Dendroidal Spaces.- 10 Reedy Categories and Diagrams of Spaces.- 11 Mapping Spaces and Bousfield Localizations.- 12 Dendroidal Spaces and ∞-Operads.- 13 Left Fibrations and the Covariant Model Structure.- 14 Simplicial Operads and ∞-Operads.- Epilogue.- References.- Index.