2015/05/31 by C. Barwick, S. Glasman, J. Shah · 2 citations
Mathematics · #math.AT #math.CT #math.KT
paper · pdf · doi:10.2140/tunis.2020.2.97
published as Tunisian J. Math. 2 (2020) 97-146 · 40 pages. v2: New authors added; somewhat awkward case-based system for the operad structures on effective Burnside infinity-categories from the previous version now streamlined, thanks to the (new) notion of symmetric promonoidal infinity-category
arxiv created 2016/03/29 · arxiv updated 2019/04/03
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 A. 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 category of finite G-sets is simply the G-equivariant sphere spectrum.