Symmetric Powers and Norms of Mackey Functors
Symmetric Powers and Norms of Mackey Functors
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麦基函子的对称幂和范数
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发表时间：
2013
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通讯作者：
John Ullman
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作者：
John Ullman
本文给出了Mackey函子范畴上的对称幂构和范数构的推导，以及g对称一元结构的推导。我们在[Ull2]的结果的基础上，证明了有限群G上的每一个Tambara函子都是交换环G谱的第零稳定同伦群。用代数方法证明了[Ull2]中允诺的Tambara函子范畴上的范数/限制附加。最后，我们给出了用Mackey函子的乘法前推来描述Tambara函子的一个新特征，并利用这个特征得到了与等变扩展幂结构密切匹配的Mackey函子上的自由Tambara函子的一个吸引人的新描述。
In this paper we give detailed algebraic descriptions of the derived symmetric power and norm constructions on categories of Mackey functors, as well as the derived G-symmetric monoidal structure. We build on the results of [Ull2], in which it is shown that every Tambara functor over a finite group G arises as the zeroth stable homotopy group of a commutative ring G-spectrum. The norm / restriction adjunctions on categories of Tambara functors promised in [Ull2] are demonstrated algebraically. Finally, we give a new characterization of Tambara functors in terms of multiplicative push forwards of Mackey functors, and use this to obtain an appealing new description of the free Tambara functor on a Mackey functor which closely matches the structure of equivariant extended powers.