Simplicial and Dendroidal Homotopy Theory by Heuts & Moerdijk
Simplicial and Dendroidal Homotopy Theory - 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 8-Operads
13. Left Fibrations and the Covariant Model Structure
14. Simplicial Operads and 8-Operads
What You Will Learn in Simplicial and Dendroidal Homotopy Theory
"Simplicial and Dendroidal Homotopy Theory" by Gijs Heuts and Ieke Moerdijk is a modern mathematical text exploring the connections between "simplicial sets", "dendroidal sets", and "homotopy theory". The book provides a structured approach to understanding how higher categories and "8-operads" can be studied using combinatorial and algebraic tools. It is aimed at graduate students and researchers who want to bridge classical homotopy theory with contemporary developments in higher algebra.
The authors systematically build the theory, starting with "simplicial sets" and geometric realization, then moving to "dendroidal sets", which naturally model operads and higher-algebraic structures. Key topics include Kan conditions, model category structures, fibrations, and equivalences. The book emphasizes rigorous explanations while offering insight into how simplicial and dendroidal approaches interact, providing a clear path from classical topology to modern higher category theory.
With its focus on "higher algebra", 8-categories, and operads, the text serves as both a reference and a learning resource. Readers gain tools to study homotopical structures in topology, algebra, and mathematical physics. Its combination of theory, examples, and connections to current research makes it a valuable resource for anyone exploring the frontiers of algebraic topology and homotopy theory.
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 leading Dutch mathematicians known for contributions to category theory and homotopy theory. Their work provides rigorous foundations, complete proofs, and insights into modern higher category structures, making it an essential reference for anyone exploring abstract algebraic and topological structures.
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