Orbit categories, classifying spaces, and generalized homotopy fixed points

TL;DR

This paper introduces a new categorical approach to describing generalized homotopy fixed point spaces using homotopy limits over orbit categories, simplifying the understanding of classifying spaces for subgroup families.

Contribution

It provides a novel categorical model for classifying spaces and reinterprets Rosenthal's generalized homotopy fixed points as homotopy limits over orbit categories.

Findings

New categorical model for classifying spaces

Reinterpretation of homotopy fixed points as homotopy limits

Simplified description of generalized homotopy fixed point spaces

Abstract

We give a new description of Rosenthal's generalized homotopy fixed point spaces as homotopy limits over the orbit category. This is achieved using a simple categorical model for classifying spaces with respect to families of subgroups.