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 . We also answer a question of Mathew, proving that the algebraic -theory of group actions is lax symmetric monoidal. We also show that the algebraic -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 -theory of the category of finite -sets is simply the -equivariant sphere spectrum.
"Spectral Mackey functors and equivariant algebraic $K$-theory, II." Tunisian J. Math. 2 (1) 97 - 146, 2020. https://doi.org/10.2140/tunis.2020.2.97