Tambara Functors and Commutative Ring Spectra
Tambara Functors and Commutative Ring Spectra
复制标题
Tambara 函子和交换环谱
DOI：
--
复制
发表时间：
2013
期刊：
影响因子：
--
通讯作者：
John Ullman
中科院分区：
文献类型：
--
作者：
John Ullman
众所周知，真正的等变交换环谱的第零个稳定同伦群具有乘法传递（范数），使其成为 Tambara 函子。我们在这里证明所有 Tambara 函子都可以通过这种方式获得。事实上，我们证明了Eilenberg MacLane交换环谱的同伦范畴等价于Tambara函子的范畴。 Tambara 函子的几个代数结果作为推论而导出。最后，当群非平凡时，我们排除了 Eilenberg MacLane 谱的松散对称幺半群构造的存在。
It is well known that the zeroth stable homotopy group of a genuine equivariant commutative ring spectrum has multiplicative transfers (norms), making it into a Tambara functor. We prove here that all Tambara functors can be obtained in this way. In fact, we prove that the homotopy category of Eilenberg MacLane commutative ring spectra is equivalent to the category of Tambara functors. Several algebraic results on Tambara functors are derived as corollaries. Finally, we rule out the existence of a lax symmetric monoidal construction for Eilenberg MacLane spectra when the group is nontrivial.