Simplicial and Dendroidal Homotopy Theory

This open access book offers a self-contained introduction to the homotopy theory of simplicial and dendroidal sets and spaces. 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.

• | Author: Gijs Heuts, Ieke Moerdijk
• | Publisher: Springer International Publishing AG
• | Publication Date: Aug 03, 2022
• | Number of Pages:
• | Language:
• | Binding: Hardback
• | ISBN-13: 9783031104466
• | ISBN-10: 3031104463