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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| Superior document: | Ergebnisse der Mathematik und ihrer Grenzgebiete v.75 |
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| Place / Publishing House: | Cham : : Springer International Publishing AG,, 2022. ©2022. |
| Year of Publication: | 2022 |
| Language: | English |
| Series: | Ergebnisse der Mathematik und ihrer Grenzgebiete
75. |
| Physical Description: | 1 online resource (xx, 612 pages) :; illustrations. |
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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