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  3. Homotopy Theory of Enriched Mackey Functors
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2025
      February 2025
      ISBN:
      9781009519564
      9781009519526
      DOI:
      https://doi.org/10.1017/9781009519564
      Dimensions:
      Weight & Pages:
      Dimensions:
      (229 x 152 mm)
      Weight & Pages:
      0.73kg, 523 Pages
      • Subjects:
      Mathematics (general), Mathematics, Geometry and Topology
      Series:
      London Mathematical Society Lecture Note Series (492)
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    Subjects:
    Mathematics (general), Mathematics, Geometry and Topology
    Series:
    London Mathematical Society Lecture Note Series (492)
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    Book description

    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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