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. 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...
| Main Authors: | , |
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| Format: | eBook |
| Language: | English |
| Published: |
Cham
Springer International Publishing
2022, 2022
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| Edition: | 1st ed. 2022 |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
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