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
5 - Pointed Multicategories and M1–Modules Model All Connective Spectra
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 extends the material of Chapter 3 to a pointed free construction from pointed multicategories to permutative categories. This is not a restriction, along the inclusion of pointed multicategories among all multicategories, but an extension, along the functor that adjoins a disjoint basepoint. Essential results, such as the adjunction with the endomorphism construction and compatibility with stable equivalences, are likewise extended from Chapter 3.
Keywords
- Type
- Chapter
- Information
- Homotopy Theory of Enriched Mackey FunctorsClosed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors, pp. 111 - 144Publisher: Cambridge University PressPrint publication year: 2025