230 citations · 1.2k across the 72 of their papers we have counts for
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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…
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…
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…
Multicategories Model All Connective Spectra
Niles Johnson, Donald Yau
There is a free construction from multicategories to permutative categories, left adjoint to the endomorphism multicategory construction. The main result shows that these functors…
Multifunctorial Inverse -Theory
Niles Johnson, Donald Yau
We show that Mandell's inverse -theory functor is a categorically-enriched non-symmetric multifunctor. In particular, it preserves algebraic structures parametrized by non-symme…
A graphical category for higher modular operads
Philip Hackney, Marcy Robertson, Donald Yau
We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Qui…