In a braided rigid monoidal category $(\mathcal{M},\otimes)$ left and right duals coincide. What is an example of a rigid monoidal category where left and right duals coincide but there exist no braiding for the category?



Nonbraided rigid monoidal category where left and right duals coincide
The simplest example is G-graded vector spaces where G is a non-abelian group.


