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2020 Spectral Mackey functors and equivariant algebraic $K$-theory, II
Clark Barwick, Saul Glasman, Jay Shah
Tunisian J. Math. 2(1): 97-146 (2020). DOI: 10.2140/tunis.2020.2.97

Abstract

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.

Citation

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Clark Barwick. Saul Glasman. Jay Shah. "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

Information

Received: 30 July 2018; Revised: 11 December 2018; Accepted: 27 December 2018; Published: 2020
First available in Project Euclid: 2 April 2019

zbMATH: 07074072
MathSciNet: MR3933393
Digital Object Identifier: 10.2140/tunis.2020.2.97

Subjects:
Primary: 19D99, 55P91

Rights: Copyright © 2020 Mathematical Sciences Publishers

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