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
- 2 Categorically Enriched Multicategories
- 3 Infinite Loop Space Machines
- 4 Homotopy Theory of Multicategories
- Part 2 Homotopy Theory Of Pointed Multicategories, M1 –Modules, And Permutative Categories
- 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
4 - Homotopy Theory of Multicategories
from Part 1 - Background On Multicategories And K –Theory Functors
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
- 2 Categorically Enriched Multicategories
- 3 Infinite Loop Space Machines
- 4 Homotopy Theory of Multicategories
- Part 2 Homotopy Theory Of Pointed Multicategories, M1 –Modules, And Permutative Categories
- 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 reviews equivalences of homotopy theories between Multicat, the category of small multicategories and multifunctors, PermCat^st, the category of small permutative categories and strict monoidal functors, and PermCat^su, the category of small permutative categories and strictly unital symmetric monoidal functors. These equivalences are given by a free left adjoint to the endomorphism functor. This material provides an important foundation for that of Part 2.
Keywords
- Type
- Chapter
- Information
- Homotopy Theory of Enriched Mackey FunctorsClosed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors, pp. 83 - 108Publisher: Cambridge University PressPrint publication year: 2025