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.

• 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.

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.

• 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.

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.

• 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.