Spectral Mackey functors and equivariant algebraic K-theory (II)

Clark Barwick, Saul Glasman, Jay Shah

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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 category of finite G -sets is simply the G -equivariant sphere spectrum.
Original languageEnglish
Article number1
Pages (from-to)97-146
Number of pages53
JournalTunisian Journal of Mathematics
Publication statusPublished - 22 Mar 2019


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