Nonassociative geometry in quasi-Hopf representation categories II: Connections and curvature

Understand

We continue our systematic development of noncommutative and nonassociative differential geometry internal to the representation category of a quasitriangular quasi-Hopf algebra.

• We describe derivations, differential operators, differential calculi and connections using universal categorical constructions to capture algebraic properties such as Leibniz rules.
• Our main result is the construction of morphisms which provide prescriptions for lifting connections to tensor products and to internal homomorphisms.
• We describe the curvatures of connections within our formalism, and also the formulation of Einstein-Cartan geometry as a putative framework for a nonassociative theory of gravity.