# Free incomplete Tambara functors are almost never flat

@inproceedings{Hill2021FreeIT, title={Free incomplete Tambara functors are almost never flat}, author={Michael A. Hill and David Mehrle and J. D. Quigley}, year={2021} }

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 functors play the role of modules. Surprisingly, free incomplete Tambara functors often fail to be free as Mackey functors. In this paper, we determine for all finite groups conditions under which a free incomplete Tambara functor is free as a Mackey functor. For solvable groups, we show that a free incomplete…

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Real topological Hochschild homology via the norm and Real Witt vectors

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## References

SHOWING 1-10 OF 54 REFERENCES

On the André–Quillen homology of Tambara functors

- Mathematics
- 2017

Abstract We lift to equivariant algebra three closely related classical algebraic concepts: abelian group objects in augmented commutative algebras, derivations, and Kahler differentials. We define…

Tambara functors

- Mathematics
- 2012

We survey and extend the theory of Tambara functors. These are algebraic structures similar to Mackey functors, but with multiplicative norm maps as well as additive transfer maps, and a rule…

Incomplete Tambara functors

- Mathematics
- 2016

For a "genuine" equivariant commutative ring spectrum $R$, $\pi_0(R)$ admits a rich algebraic structure known as a Tambara functor. This algebraic structure mirrors the structure on $R$ arising from…

SPECTRAL MACKEY FUNCTORS AND EQUIVARIANT ALGEBRAIC K-THEORY (I)

- 2016

Spectral Mackey functors are homotopy-coherent versions of ordinary Mackey functors as defined by Dress. We show that they can be described as excisive functors on a suitable∞-category, and we use…

The right adjoint to the equivariant operadic
forgetful functor on incomplete Tambara
functors

- MathematicsHomotopy Theory: Tools and Applications
- 2019

For $N_\infty$ operads $\mathcal O$ and $\mathcal O'$ such that there is an inclusion of the associated indexing systems, there is a forgetful functor from incomplete Tambara functors over $\mathcal…

The structure of Mackey functors

- Mathematics
- 1995

Keywords: blocks ; finite groups ; category of finite $G$-sets ; diagrams of $G$-sets ; category of Mackey functors ; category of modules ; path algebras ; quiver with relations ; composition factors…

Simple Mackey functors

- Mathematics
- 1990

Keywords: restriction ; transfer ; Mackey functors ; Burnside ring ; Green ring ; Grothendieck ring functor ; cohomology group functor ; abelian category ; induction ; inflation ; simple objects…

The Witt vectors for Green functors

- MathematicsJournal of Algebra
- 2019

We define twisted Hochschild homology for Green functors. This construction is the algebraic analogue of the relative topological Hochschild homology $THH_{C_n}(-)$, and it describes the $E_2$ term…

Operadic multiplications in equivariant spectra, norms, and transfers

- Mathematics
- 2013

We study homotopy-coherent commutative multiplicative structures on equivariant spaces and spectra. We define N-infinity operads, equivariant generalizations of E-infinity operads. Algebras in…