论文标题
bi-Incomplete tambara functors作为$ \ MATHCAL {O} $ - 交换性monoids
Bi-incomplete Tambara functors as $\mathcal{O}$-commutative monoids
论文作者
论文摘要
Tambara函子是对环的概括性的概括，这些环是真正的均值换向环光谱的同型组。在最近的工作中，Blumberg和Hill研究了相应的代数结构，称为Bi-Complete Tambara Foundors，这些结构是由在不完整的$ G $ Universes上索引的环光谱引起的。在本文中，我们通过证明了霍耶尔（Hoyer）的概括 - 马祖尔定理（Mazur Therorem）在双重份额的环境中，回答了Blumberg和Hill的猜想。 Bi-Complete Tambara函子的特征是索引类别，这些类别将不完整的规范和传输系统参数化。在我们的工作过程中，我们开发了几种研究这些索引类别的新工具。特别是，我们提供了一个易于检查的，何时在Blumberg和Hill兼容两个索引类别时的组合表征。
Tambara functors are an equivariant generalization of rings that appear as the homotopy groups of genuine equivariant commutative ring spectra. In recent work, Blumberg and Hill have studied the corresponding algebraic structures, called bi-incomplete Tambara functors, that arise from ring spectra indexed on incomplete $G$-universes. In this paper, we answer a conjecture of Blumberg and Hill by proving a generalization of the Hoyer--Mazur theorem in the bi-incomplete setting. Bi-incomplete Tambara functors are characterized by indexing categories which parameterize incomplete systems of norms and transfers. In the course of our work, we develop several new tools for studying these indexing categories. In particular, we provide an easily checked, combinatorial characterization of when two indexing categories are compatible in the sense of Blumberg and Hill.
