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
- 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
7 - Multicategorically Enriched Categories
from Part 3 - Enrichment Of Diagrams And Mackey Functors In Closed Multicategories
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
- 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 gives the basic definitions and results for enrichment in a nonsymmetric multicategory M. Proposition 6.2.1 shows that this material agrees, in the case that M is the endomorphism multicategory of a monoidal category, with classical enriched category theory over V. The main application takes M to be the multicategory of permutative categories and strictly unital symmetric monoidal functors, which is not an endomorphism multicategory. Sections 6.3 through 6.5 treat this case in detail.
Keywords
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- Information
- Homotopy Theory of Enriched Mackey FunctorsClosed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors, pp. 167 - 209Publisher: Cambridge University PressPrint publication year: 2025