Homotopy Theory of Enriched Mackey Functors Closed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors
Book contents
- London Mathematical Society Lecture Note Series
- Frontmatter
- Dedication
- Contents
- List of Main Facts
- List of Notations
- Preface
- 1 Motivations from Equivariant Topology
- Part 1 Background On Multicategories And K –Theory Functors
- Part 2 Homotopy Theory Of Pointed Multicategories, M1 –Modules, And Permutative Categories
- 5 Pointed Multicategories and M1–Modules Model All Connective Spectra
- 6 Multiplicative Homotopy Theory of Pointed Multicategories and M1–Modules
- Part 3 Enrichment Of Diagrams And Mackey Functors In Closed Multicategories
- Part 4 Homotopy Theory Of Enriched Diagrams And Mackey Functors
- Appendix A Categories
- Appendix B Enriched Category Theory
- Appendix C Multicategories
- Appendix D Open Questions
- Bibliography
- Index
6 - Multiplicative Homotopy Theory of Pointed Multicategories and M1–Modules
from Part 2 - Homotopy Theory Of Pointed Multicategories, M1 –Modules, And Permutative Categories
Published online by Cambridge University Press: 16 January 2025
Book contents
- London Mathematical Society Lecture Note Series
- Frontmatter
- Dedication
- Contents
- List of Main Facts
- List of Notations
- Preface
- 1 Motivations from Equivariant Topology
- Part 1 Background On Multicategories And K –Theory Functors
- Part 2 Homotopy Theory Of Pointed Multicategories, M1 –Modules, And Permutative Categories
- 5 Pointed Multicategories and M1–Modules Model All Connective Spectra
- 6 Multiplicative Homotopy Theory of Pointed Multicategories and M1–Modules
- Part 3 Enrichment Of Diagrams And Mackey Functors In Closed Multicategories
- Part 4 Homotopy Theory Of Enriched Diagrams And Mackey Functors
- Appendix A Categories
- Appendix B Enriched Category Theory
- Appendix C Multicategories
- Appendix D Open Questions
- Bibliography
- Index
Summary
This chapter shows that the pointed free construction from Chapter 4 is a nonsymmetric multifunctor. Furthermore, it provides equivalences of homotopy theories between categories of nonsymmetric algebras in pointed multicategories and permutative categories. This is the basis for applications to enriched diagrams in Chapter 12.
- Type
- Chapter
- Information
- Homotopy Theory of Enriched Mackey FunctorsClosed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors, pp. 145 - 164Publisher: Cambridge University PressPrint publication year: 2025