Categorical models for equivariant classifying spaces

TL;DR

This paper provides simple categorical models for equivariant classifying spaces, which are essential for advancing theories in equivariant infinite loop spaces and algebraic K-theory, and are also valuable in bundle and covering space theories.

Contribution

It introduces new, simple categorical models of equivariant classifying spaces, facilitating progress in equivariant topology and related fields.

Findings

Models are simple and precise.

Applicable to equivariant infinite loop space theory.

Useful in equivariant bundle and covering space theory.

Abstract

Starting categorically, we give simple and precise models of equivariant classifying spaces. We need these models for work in progress in equivariant infinite loop space theory and equivariant algebraic K-theory, but the models are of independent interest in equivariant bundle theory and especially equivariant covering space theory.