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
- Part 3 Enrichment Of Diagrams And Mackey Functors In Closed Multicategories
- Part 4 Homotopy Theory Of Enriched Diagrams And Mackey Functors
- 12 Homotopy Equivalences between Enriched Diagram and Mackey Functor Categories
- 13 Applications to Multicategories and Permutative Categories
- Appendix A Categories
- Appendix B Enriched Category Theory
- Appendix C Multicategories
- Appendix D Open Questions
- Bibliography
- Index
13 - Applications to Multicategories and Permutative Categories
from Part 4 - Homotopy Theory Of Enriched Diagrams And Mackey 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
- 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
- 12 Homotopy Equivalences between Enriched Diagram and Mackey Functor Categories
- 13 Applications to Multicategories and Permutative Categories
- Appendix A Categories
- Appendix B Enriched Category Theory
- Appendix C Multicategories
- Appendix D Open Questions
- Bibliography
- Index
Summary
This chapter applies the general theory from Chapter 11 to change of enrichment along the inverse equivalences of homotopy theories developed in Part 2. The main results, Theorems 12.1.6, 12.4.6, and 12.6.6, establish equivalences of homotopy theories for enriched diagram categories and Mackey functor categories over pointed multicategories, permutative categories, and M1-modules.
Keywords
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- Chapter
- Information
- Homotopy Theory of Enriched Mackey FunctorsClosed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors, pp. 368 - 400Publisher: Cambridge University PressPrint publication year: 2025