Equivariant complete Segal spaces

TL;DR

This paper develops a new model for equivariant $( abla, 1)$-categories by adapting existing approaches for simplicial spaces and modifying Segal and completeness conditions to incorporate group actions.

Contribution

It introduces an equivariant model for $( abla, 1)$-categories based on simplicial spaces, extending prior non-equivariant models.

Findings

Provides a new framework for equivariant $( abla, 1)$-categories.

Adapts Rezk's Segal and completeness conditions for the equivariant setting.

Extends Shimakawa's approach for equivariant $ abla$-spaces.

Abstract

In this paper we give a model for equivariant $(\infty, 1)$-categories. We modify an approach of Shimakawa for equivariant $\Gamma$-spaces to the setting of simplicial spaces. We then adapt Rezk's Segal and completeness conditions to fit with this setting.