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2 results

  • 12 - Homotopy Equivalences between Enriched Diagram and Mackey Functor Categories

  • from Part 4 - Homotopy Theory Of Enriched Diagrams And Mackey Functors
  • Niles Johnson, Ohio State University, Donald Yau, Ohio State University
  • Book:
    Homotopy Theory of Enriched Mackey Functors
    Published online:
    16 January 2025
    Print publication:
    06 February 2025, pp 331-367

  • Summary

    This chapter establishes the general theory for a pair of nonsymmetric multifunctors (E,F) to provide inverse equivalences of homotopy theories between enriched diagram categories. The main result is Theorem 11.4.14 and does not require E or F to satisfy the symmetry condition of a multifunctor. A similar result for enriched Mackey functor categories, in Theorem 11.4.24, requires that E, but not necessarily F, is a multifunctor. This is important for the applications, Theorems 12.1.6 and 12.4.6. There, E is an endomorphism multifunctor and F is a corresponding free nonsymmetric multifunctor.

  • 8 - Change of Multicategorical Enrichment

  • from Part 3 - Enrichment Of Diagrams And Mackey Functors In Closed Multicategories
  • Niles Johnson, Ohio State University, Donald Yau, Ohio State University
  • Book:
    Homotopy Theory of Enriched Mackey Functors
    Published online:
    16 January 2025
    Print publication:
    06 February 2025, pp 210-228

  • Summary

    This chapter develops the first collection of results around change of enrichment along a (possibly nonsymmetric) multifunctor. As in Chapter 6, it is shown that this theory extends the classical theory for enrichment over (possibly symmetric) monoidal categories. Compositionality and 2-functoriality for the change-of-enrichment constructions are treated in Sections 7.4 and 7.5, respectively.