Global algebraic K-theory

Abstract

We introduce a global equivariant refinement of algebraic K-theory; here `global equivariant' refers to simultaneous and compatible actions of all finite groups. Our construction turns a specific kind of categorical input data into a global $\Omega$-spectrum that keeps track of genuine $G$-equivariant infinite loop spaces, for all finite groups $G$. The resulting global algebraic K-theory spectrum is a rigid way of packaging the representation K-theory, or `Swan K-theory' into one highly structured object.

References in corpus (2)

• An Inverse K-Theory Functor
• Homotopy invariance of convolution products

Cited by in corpus (5)

• G-Global Homotopy Theory and Algebraic K-Theory
• On the global homotopy theory of symmetric monoidal categories
• Genuine vs. naïve symmetric monoidal G-categories
• Algebraic K${}_0$ for unpointed Categories
• Categorical models of unstable G-global homotopy theory