Spectral Mackey functors and equivariant algebraic $K$-theory, II
作者: Clark BarwickSaul GlasmanJay Shah
刊名: Tunisian Journal of Mathematics, 2020, Vol.2 (1), pp.97-146
来源数据库: Project Euclid
DOI: 10.2140/tunis.2020.2.97
关键词: Spectral Mackey functorsSpectral Green functorsEquivariant algebraic $K\mkern-2mu$-theoryDay convolutionSymmetric promonoidal infinity-categoriesEquivariant Barratt–Priddy–Quillen
原始语种摘要: We study the “higher algebra” of spectral Mackey functors, which the first named author introduced in Part I of this paper. In particular, armed with our new theory of symmetric promonoidal ∞ -categories and a suitable generalization of the second named author’s Day convolution, we endow the ∞ -category of Mackey functors with a well-behaved symmetric monoidal structure. This makes it possible to speak of spectral Green functors for any operad O . We also answer a question of Mathew, proving that the algebraic K -theory of group actions is lax symmetric monoidal. We also show that the algebraic K -theory of derived stacks provides an example. Finally, we give a very short, new proof of the equivariant Barratt–Priddy–Quillen theorem, which states that the algebraic K -theory of the...
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  • algebraic 代数的
  • II Interactive Interface
  • theory 理论
  • convolution 褶积
  • spectral 谱的
  • author 著者
  • proof 证明
  • named 命名
  • infinity 无穷限大
  • sphere