Simplicial and dendroidal homotopy theory

Simplicial and dendroidal homotopy theory / Gijs Heuts, Ieke Moerdijk.

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 th...

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Bibliographic Details
Main Authors: Heuts, Gijs (Author), Moerdijk, Ieke (Author)
Format: eBook
Language:English
Published: Cham, Switzerland : Springer, 2022.
Series:Ergebnisse der Mathematik und ihrer Grenzgebiete ; 3. Folge, Bd. 75.
Subjects:
Homotopy theory.
Homotopy theory
Teoria de l'homotopia.
Llibres electrònics.
Online Access:Click for online access
Table of Contents:
  • 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.

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