  We use the string diagram calculus to give graphical proofs of the basic
results of Etingof, Nikshych and Ostrik on fusion categories. These results
include: the quadruple dual is canonically isomorphic to the identity,
positivity of the paired dimensions, and Ocneanu rigidity. We introduce the
pairing convention as a convenient graphical framework for working with fusion
categories. We use this framework to express the pivotal operators as a product
of the apex associator monodromy and the pivotal indicators. We also
characterize pivotal structures as solutions of an explicit set of algebraic
equations over the complex numbers.
