Simplicial and Dendroidal Homotopy Theory by Heuts & Moerdijk

Book 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

About this book :-
"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 Detail :-
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 Author :-
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.

Similar Topology Books