Constructing TQFTs Using Non-Hermitian Ribbon Fusion Categories

In this paper, we provide a construction of a Topological Quantum Field Theory from a Non-Hermitian Ribbon Fusion Category. This is a simple method that does not involve enriching over Fusion Categories, or using other complicated structures. To substantiate this construction, we also prove theorems on the Müger center, braiding, and spherical structure of such a fusion category.