Homotopy Theory of Enriched Mackey Functors

Auteur
Niles Johnson is an Associate Professor of Mathematics at the Ohio State University at Newark. His research focuses on algebraic topology. Donald Yau is a Professor of Mathematics at the Ohio State University at Newark. His research focuses on homotopy theory and algebraic K-theory.

Texte du rabat
A detailed treatment of Mackey functors and homotopical applications in the broader context of enriched diagram categories, suitable for graduate students or researchers with an interest in category theory, equivariant homotopy theory, or related fields. A self-contained reference, with complete definitions and full proofs for non-expert readers.

Contenu

1. Motivations from equivariant topology; Part I. Background on Multicategories and K-Theory Functors: 2. Categorically enriched multicategories; 3. Infinite loop space machines; 4. Homotopy theory of multicategories; Part II. 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 III. 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 IV. 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; Appendices: A. Categories; B. Enriched category theory; C. Multicategories; D. Open questions; Bibliography; Index.