Equivariant symmetric monoidal structures

By M. Hill, M. Hopkins. 2016

51 citations recorded by the source corpus.

Building on structure observed in equivariant homotopy theory, we define an equivariant generalization of a symmetric monoidal category: a $G$-symmetric monoidal category. These record not only the symmetric monoidal products but also symmetric monoidal powers indexed by arbitrary finite $G$-sets. We then define $G$-commutative monoids to be the natural extension of ordinary commutative monoids to this new context. Using this machinery, we then describe when Bousfield localization in equivariant spectra preserves certain operadic algebra structures, and we explore the consequences of our definitions for categories of modules over a $G$-commutative monoid.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d42aa863bd20fabd5f3a6583732e9899e9518510

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Incomplete Tambara functors (2016, methodology): “This classification gives a conceptual justification for our prior description of N∞ operads and also allows us to easily describe the properties of the category of incomplete Tambara functors.”
An equivariant tensor product on Mackey functors (2015, background): “s. We will then show that G-Tambara functors are the Gcommutative monoids under this structure, thus proving Theorem 1.1. We begin with Hill and Hopkins’ deﬁnition of a G-symmetric monoidal structure [HH16]. Deﬁnition 5.1. Let SetFin,Iso G be the category whose objects are ﬁnite Gsets and whose morp”