Homotopy theory with *categories

TL;DR

This paper develops model category structures for marked *-categories to facilitate the study of their associated infinity categories, enabling explicit calculations of G-fixed points and G-orbits in G-equivariant settings.

Contribution

It introduces new model structures on (marked) *-categories and uses them to explicitly compute G-fixed points and G-orbits in the infinity categorical framework.

Findings

Established model category structures for (marked) *-categories.

Presented explicit calculations of G-fixed points.

Presented explicit calculations of G-orbits.

Abstract

We construct model category structures on various types of (marked) *-categories. These structures are used to present the infinity categories of (marked) *-categories obtained by inverting (marked) unitary equivalences. We use this presentation to explicitly calculate the \infty-categorical G-fixed points and G-orbits for G-equivariant (marked) *-categories.