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2 results

  • 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.

  • 13 - Applications to Multicategories and Permutative 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 368-400

  • Summary

    This chapter applies the general theory from Chapter 11 to change of enrichment along the inverse equivalences of homotopy theories developed in Part 2. The main results, Theorems 12.1.6, 12.4.6, and 12.6.6, establish equivalences of homotopy theories for enriched diagram categories and Mackey functor categories over pointed multicategories, permutative categories, and M1-modules.