Homotopy Theory of Enriched Mackey Functors: Closed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors

Niles Johnson; Donald Yau

doi:10.1017/9781009519564

Homotopy Theory of Enriched Mackey Functors

Closed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors

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This Book has been cited by the following publications. This list is generated based on data provided by Crossref.

Aldrovandi, Ettore and Lester, Cynthia 2023. On Multi-Determinant Functors for Triangulated Categories. Theory and Applications of Categories, Vol. 39, Issue. , p. 769.

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Niles Johnson, Ohio State University, Donald Yau, Ohio State University

Publisher:: Cambridge University Press
Online publication date:: January 2025
Print publication year:: 2025
Online ISBN:: 9781009519564
DOI:: https://doi.org/10.1017/9781009519564

Subjects:: Mathematics (general), Mathematics, Geometry and Topology
Series:: London Mathematical Society Lecture Note Series (492)

US$100.00

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This work develops techniques and basic results concerning the homotopy theory of enriched diagrams and enriched Mackey functors. Presentation of a category of interest as a diagram category has become a standard and powerful technique in a range of applications. Diagrams that carry enriched structures provide deeper and more robust applications. With an eye to such applications, this work provides further development of both the categorical algebra of enriched diagrams, and the homotopy theoretic applications in K-theory spectra. The title refers to certain enriched presheaves, known as Mackey functors, whose homotopy theory classifies that of equivariant spectra. More generally, certain stable model categories are classified as modules - in the form of enriched presheaves - over categories of generating objects. This text contains complete definitions, detailed proofs, and all the background material needed to understand the topic. It will be indispensable for graduate students and researchers alike.

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Homotopy Theory of Enriched Mackey Functors

Closed Multicategories, Permutative Enrichments, and Algebraic Foundations for Spectral Mackey Functors

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