Diagram categories of Brauer type

Abstract: This paper introduces monoidal (super)categories resembling the Brauer category. For all categories, we can construct bases of the hom-spaces using Brauer diagrams. These categories include the Brauer category, its deformation the BWM-category, the periplectic Brauer category, and its deformation the periplectic $q$-Brauer category but also some new exotic categories. We show that the BWM-category is the unique deformation of the Brauer category in this framework, while the periplectic Brauer category has two deformations, which are each other monoidal opposite.