Coherence for monoidal $G$-categories and braided $G$-crossed categories

TL;DR

This paper establishes a coherence theorem for group actions on monoidal categories and applies it to prove coherence for braided G-crossed categories, advancing the understanding of their structural properties.

Contribution

It introduces a coherence theorem for group actions on monoidal categories and extends it to braided G-crossed categories, providing a foundational result in category theory.

Findings

Proved a coherence theorem for group actions on monoidal categories.

Established coherence results for braided G-crossed categories.

Enhanced the theoretical framework for G-category structures.

Abstract

We prove a coherence theorem for actions of groups on monoidal categories. As an application we prove coherence for arbitrary braided $G$-crossed categories.