Homotopy Theory of Enriched 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
- 7 Multicategorically Enriched Categories
- 8 Change of Multicategorical Enrichment
- 9 The Closed Multicategory of Permutative Categories
- 10 Self-Enrichment and Standard Enrichment of Closed Multicategories
- 11 Enriched Diagrams and Mackey Functors of 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
11 - Enriched Diagrams and Mackey Functors of Closed Multicategories
from Part 3 - Enrichment Of Diagrams And Mackey Functors In Closed Multicategories
Published online by Cambridge University Press: 16 January 2025
- 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
- 7 Multicategorically Enriched Categories
- 8 Change of Multicategorical Enrichment
- 9 The Closed Multicategory of Permutative Categories
- 10 Self-Enrichment and Standard Enrichment of Closed Multicategories
- 11 Enriched Diagrams and Mackey Functors of 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 provides the main results of Part 3. These make use of the preceding material on enrichment over (closed) multicategories, and apply it to categories of enriched diagrams and enriched Mackey functors. A key detail, both here and in the homotopical applications of Part 4, is that nonsymmetric multifunctors provide a diagram change of enrichment, but not necessarily a change of enrichment for enriched Mackey functors (presheaves). The essential reason is that symmetry of a multifunctor is required for commuting the opposite construction in the domain of enriched presheaves with change of enrichment. Sections 10.5 and 10.6 give applications to Elmendorf–Mandell K-theory, with attention to the relevant symmetry conditions among other details.
Keywords
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- Information
- Homotopy Theory of Enriched Mackey FunctorsClosed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors, pp. 301 - 328Publisher: Cambridge University PressPrint publication year: 2025