论文标题
富集的Mackey函子的同型理论
Homotopy Theory of Enriched Mackey Functors
论文作者
论文摘要
Mackey Foundor提供了模棱两可的共同体学理论的系数系统。更一般而言，丰富的预志类别为许多稳定的兴趣类别提供了分类和组织。沿着$ K $的多函数更改富集为多函数提供了重要的工具，用于构建来自富含代数结构（例如置换类别）的Mackey函数的光谱Mackey函子。 这项工作详细介绍了图表，预示和Mackey函子，这些图在封闭的多材中丰富了。培养在内的富集的变化受到谨慎的态度。该框架应用于富集图和Mackey Foundor类别的同型理论，包括由$ K $ - 理论多函数引起的同质理论的等效性。感兴趣的特定应用包括图表和Mackey函数，在尖锐的多材，置换类别和对称光谱中富含。
Mackey functors provide the coefficient systems for equivariant cohomology theories. More generally, enriched presheaf categories provide a classification and organization for many stable model categories of interest. Changing enrichments along $K$-theory multifunctors provides an important tool for constructing spectral Mackey functors from Mackey functors enriched in algebraic structures such as permutative categories. This work gives a detailed development of diagrams, presheaves, and Mackey functors enriched over closed multicategories. Change of enrichment, including the relevant compositionality, is treated with care. This framework is applied to the homotopy theory of enriched diagram and Mackey functor categories, including equivalences of homotopy theories induced by $K$-theory multifunctors. Particular applications of interest include diagrams and Mackey functors enriched in pointed multicategories, permutative categories, and symmetric spectra.
