On Braiding and Dyslexia

Abstract

Braided monoidal categories have important applications in knot theory, algebraic quantum field theory, and the theory of quantum groups and Hopf algebras. We will construct a new class of braided monoidal categories. Typical examples of braided monoidal categories are the category of modules over a quasitriangular Hopf algebra and the category of comodules over a coquasitriangular Hopf algebra. We consider the notion of a commutative algebra A in such a category. The category of (left and/or right) A-modules with the tensor product over A is again a monoidal category which is not necessarily braided. However, if we restrict this category to a special class of modules which we call dyslectic then this new category of dyslectic A-modules turns out to be a braided monoidal category, too, and it is a coreflexive subcategory of all A-modules.