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math.AT2022
Homotopy Theory of Enriched Mackey Functors
Niles Johnson, Donald Yau
Mackey functors provide the coefficient systems for equivariant cohomology theories. More generally, enriched presheaf categories provide a classification and organization for many…
math.AT2022
Multifunctorial -Theory is an Equivalence of Homotopy Theories
Niles Johnson, Donald Yau
We show that each of the three -theory multifunctors from small permutative categories to -categories, -simplicial sets, and connective spectra, is…
math.AT2022
Homotopy Equivalent Algebraic Structures in Multicategories and Permutative Categories
Niles Johnson, Donald Yau
We show that the free construction from multicategories to permutative categories is a categorically-enriched non-symmetric multifunctor. Our main result then shows that the induce…