  The reflection positivity property has played a central role in both
mathematics and physics, as well as providing a crucial link between the two
subjects. In a previous paper we gave a new geometric approach to understanding
reflection positivity in terms of pictures. Here we give a transparent
algebraic formulation of our pictorial approach. We use insights from this
translation to establish the reflection positivity property for the fashionable
Levin-Wen models with respect both to vacuum and to bulk excitations. We
believe these methods will be useful for understanding a variety of other
problems.
