TL;DR
This paper characterizes crossed product tensor categories, which are graded tensor categories with invertible objects in each component, using coherent outer group actions, and describes their functors, transformations, and braidings.
Contribution
It provides a comprehensive description of crossed product tensor categories and their structures via coherent outer G-actions, advancing understanding of graded monoidal categories.
Findings
Classification of crossed product tensor categories via outer G-actions
Description of graded monoidal functors and natural transformations
Analysis of braiding structures in these categories
Abstract
A graded tensor category over a group will be called a crossed product tensor category if every homogeneous component has at least one multiplicatively invertible object. Our main result is a description of the crossed product tensor categories, graded monoidal functors, monoidal natural transformations, and braiding in terms of coherent outer -actions over tensor categories.
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