On the AndreQuillen homology of Tambara functors
Abstract
We lift to equivariant algebra three closely related classical algebraic concepts: abelian group objects in augmented commutative algebras, derivations, and Kähler differentials. We define Mackey functor objects in the category of Tambara functors augmented to a fixed Tambara functor $\underline{R}$, and we show that the usual squarezero extension gives an equivalence of categories between these Mackey functor objects and ordinary modules over $\underline{R}$. We then describe the natural generalization to Tambara functors of a derivation, building on the intuition that a Tambara functor has products twisted by arbitrary finite $G$sets, and we connect this to squarezero extensions in the expected way. Finally, we show that there is an appropriate form of Kähler differentials which satisfy the classical relation that derivations out of $\underline{R}$ are the same as maps out of the Kähler differentials.
 Publication:

arXiv eprints
 Pub Date:
 January 2017
 arXiv:
 arXiv:1701.06219
 Bibcode:
 2017arXiv170106219H
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Group Theory;
 Mathematics  KTheory and Homology