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Homotopy theory of enriched Mackey functors : closed multicategories, permutative enrichments, and algebraic foundations for spectral Mackey functors / Niles Johnson, Donald Yau.
Math/Physics/Astronomy Library QA169 .J595 2025
Available
- Format:
- Book
- Author/Creator:
- Johnson, Niles, author.
- Yau, Donald Y. (Donald Ying), 1977- author.
- Series:
- London Mathematical Society lecture note series ; 492.
- London Mathematical Society lecture note series ; 492
- Language:
- English
- Subjects (All):
- Functor theory.
- Homotopy theory.
- Categories (Mathematics).
- Physical Description:
- xxxix, 483 pages : illustrations ; 23 cm
- Place of Publication:
- Cambridge, United Kingdom ; New York, NY : Cambridge University Press, 2025.
- Summary:
- "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"-- Provided by publisher.
- Contents:
- Motivations from equivariant topology
- Part 1 : Background on multicategories and k-theory functors
- Categorically enriched multicategories
- Infinite loop space machines
- Homotopy theory of multicategories
- Part 2 : Homotopy theory of pointed multicategories, M1-modules, and permutative categories
- Pointed multicategories and M1-modules model all connective spectra
- Multiplicative homotopy theory of pointed multicategories and M1-modules
- Part 3 : Enrichment of diagrams and Mackey functions in closed multicategories
- Multicategory enriched categories
- Change of multicategorical enrichment
- The closed multicategory of permutative categories
- Self-enrichment and standard enrichment of closed multicategories
- Enriched diagrams and Mackey functors of closed multicategories
- Part 4 : Homotopy theory of enriched diagrams and Mackey functors
- Homotopy equivalences between enriched diagram and Mackey functor categories
- Applications to multicategories and permutative categories
- Appendices
- A. Categories
- B. Enriched category theory
- C. Multicategories
- D. Open questions.
- Notes:
- Includes bibliographical references (pages 470-474) and index.
- ISBN:
- 9781009519526
- 1009519522
- OCLC:
- 1460918851
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