The Condensed Fiber Product and Zesting

TL;DR

This paper introduces the condensed fiber product for $G$-crossed braided fusion categories, linking it to zesting and establishing a monoidal structure on certain 2-categories, thus generalizing existing mathematical frameworks.

Contribution

It generalizes the concept of fiber products in $G$-crossed categories and connects it to cohomological zesting, providing a new monoidal structure in the theory.

Findings

Defines the condensed fiber product for $G$-crossed braided fusion categories

Shows the relation between the condensed fiber product and zesting

Establishes a monoidal structure on the 2-category of extensions

Abstract

We introduce the condensed fiber product of two $G$-crossed braided fusion categories, generalizing existing constructions in the literature. We show that this product is closely related to the cohomological construction known as zesting. Furthermore, the condensed fiber product defines a monoidal structure on the 2-category of $G$-crossed and braided extensions of braided categories with a fixed transparent symmetric pointed subcategory.