Rigid monoidal category

Summary

A rigid monoidal category, also called an autonomous category, is a monoidal category in which every object has a left and a right dual object. The main example is the category of finite-dimensional vector spaces, and more generally of finite-dimensional representations of a group. Rigidity gives every morphism a transpose, and in the braided case it allows traces and dimensions. Fusion categories and Tannakian categories are rigid by definition.