21 citations · 38 across the 14 of their papers we have counts for
10 papers · 1 filter
Partition functors and universal exponential relations
David Mehrle, Millie Rose, Nathaniel Stapleton
We introduce partition functors: algebraic structures indexed by partitions of finite sets and equipped with restriction and transfer maps along refinements. We construct a monad P…
Composition of bispans of -sets and plethysm
Nathan Cornelius, Evan Franchere, Usman Hafeez +4
Let be the Grothendieck ring of the semiring of endomorphisms of the point in the -category of bispans of finite -sets for a finite group . This is the bispan analo…
Realizing compatible pairs of transfer systems by combinatorial -operads
David Chan, Myungsin Cho, David Mehrle +4
We investigate how the notions of pairings of operads of May and compatible pairs of indexing systems of Blumberg--Hill relate via the correspondence between indexing systems and $…
The -graded homotopy of Klein-four normed Mackey functors
Bertrand J. Guillou, Jesse Keyes, David Mehrle
We compute the -graded coefficients of the equivariant Eilenberg-Mac Lane spectrum associated to various Hill-Hopkins-Ravenel norms of the constant-…
The spectrum of the Burnside Tambara functor
Maxine Elena Calle, David Chan, David Mehrle +3
We compute the spectrum of prime ideals in the Burnside Tambara functor over an arbitrary finite group. Our proof uses recent advances in the commutative algebra of Tambara functor…
On the Tambara Affine Line
David Chan, David Mehrle, J. D. Quigley +2
Tambara functors are the analogue of commutative rings in equivariant algebra. Nakaoka defined ideals in Tambara functors, leading to the definition of the Nakaoka spectrum of prim…
Pathological Computations of Mackey Functor-valued Tor over Cyclic Groups
David Mehrle, J. D. Quigley, Michael Stahlhauer
We compute Mackey functor-valued Tor over certain free incomplete Tambara functors, generalizing the computation of Tor over a polynomial ring on one generator. In contrast with th…
Koszul Resolutions over Free Incomplete Tambara Functors for Cyclic -Groups
David Mehrle, J. D. Quigley, Michael Stahlhauer
In equivariant algebra, Mackey functors replace abelian groups and incomplete Tambara functors replace commutative rings. In this context, we prove that equivariant Hochschild homo…
The homotopy of the KU_G-local equivariant sphere spectrum
Tanner N. Carawan, Rebecca Field, Bertrand J. Guillou +2
We compute the homotopy Mackey functors of the -local equivariant sphere spectrum when is a finite -group for an odd prime , building on the degree zero case from a…
Free incomplete Tambara functors are almost never flat
Michael A. Hill, David Mehrle, J. D. Quigley
Free algebras are always free as modules over the base ring in classical algebra. In equivariant algebra, free incomplete Tambara functors play the role of free algebras and Mackey…