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Homotopy Theory of Enriched Mackey Functors from Part 3 - Enrichment Of Diagrams And Mackey Functors In Closed Multicategories
Published online by Cambridge University Press: 16 January 2025
This chapter provides the main results of Part 3. These make use of the preceding material on enrichment over (closed) multicategories, and apply it to categories of enriched diagrams and enriched Mackey functors. A key detail, both here and in the homotopical applications of Part 4, is that nonsymmetric multifunctors provide a diagram change of enrichment, but not necessarily a change of enrichment for enriched Mackey functors (presheaves). The essential reason is that symmetry of a multifunctor is required for commuting the opposite construction in the domain of enriched presheaves with change of enrichment. Sections 10.5 and 10.6 give applications to Elmendorf–Mandell K-theory, with attention to the relevant symmetry conditions among other details.
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