Simplicial and Dendroidal Homotopy Theory by Heuts & Moerdijk
Simplicial and Dendroidal Homotopy Theory - Table of Contents
PART I: ELEMENTARY THEORY OF SIMPLICIAL & 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: HOMOTOPY THEORY OF SIMPLICIAL & DENDROIDAL SETS
- 7. Model Categories
- 8. Model Structures on Simplicial Sets
- 9. Model Structures on Dendroidal Sets
PART III: HOMOTOPY THEORY OF SPACES & OPERADS
- 10. Reedy Categories and Diagrams of Spaces
- 11. Mapping Spaces and Bousfield Localizations
- 12. Dendroidal Spaces and $\infty$-Operads
- 13. Left Fibrations and Covariant Model Structure
- 14. Simplicial Operads and $\infty$-Operads
What You Will Learn in Simplicial and Dendroidal Homotopy Theory
Simplicial and Dendroidal Homotopy Theory by Gijs Heuts and Ieke Moerdijk is an authoritative advanced treatise that provides a systematic foundation for the homotopy theory of operads and higher-categorical structures. This comprehensive volume guides readers through simplicial sets, tree-like dendroidal sets, Kan complexes, and Bousfield localizations with exceptional mathematical precision and clarity.
Designed for graduate students, algebraic topologists, and higher category theorists, this foundational volume bridges classical homotopical algebra and modern $\infty$-operad theory. The authors present step-by-step developments of model category structures, Reedy categories, and covariant fibrations. Whether you are studying quasi-categories, tree-indexed tensor products, or non-symmetric operads, this text offers an indispensable roadmap.
Recognized globally as the definitive reference in dendroidal homotopy theory, it remains one of the best higher category theory books for self-study. By balancing abstract operadic machinery with clear categorical intuition, it serves as an essential tool for mastering modern homotopy theory with confidence.
Book Details & Specifications
Title:
Simplicial and Dendroidal Homotopy Theory by Heuts & Moerdijk
Publisher:
Springer
Year:
2022
Pages:
622
Type:
PDF
Language:
English
ISBN-10 #:
3031104463
ISBN-13 #:
978-3031104466
License:
CC BY 4.0
Amazon:
Amazon
About the Author: Gijs Heuts and Ieke Moerdijk
The author Gijs Heuts and Ieke Moerdijk
are world-renowned Dutch mathematicians who have made pioneering contributions to algebraic topology, category theory, and differential geometry. Moerdijk, a professor at Utrecht University and member of the Royal Netherlands Academy of Arts and Sciences, co-created dendroidal sets to extend simplicial methods to operads. Heuts, a professor at Utrecht University, is a leading expert in higher category theory and chromatic homotopy theory.
Together, Heuts and Moerdijk authored Simplicial and Dendroidal Homotopy Theory to present the first unified, comprehensive account of dendroidal structures and $\infty$-operads. Their rigorous exposition and deep structural insight make this volume a classic reference for higher operad theory that continues to shape modern algebraic topology worldwide.
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