The Condensed Fiber Product and Zesting

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.