  In our previous article [arXiv:1607.06041], we established an equivalence
between pointed pivotal module tensor categories and anchored planar algebras.
This article introduces the notion of unitarity for both module tensor
categories and anchored planar algebras, and establishes the unitary analog of
the above equivalence. Our constructions use Baez's 2-Hilbert spaces (i.e.,
semisimple $C^*$-categories equipped with unitary traces), the unitary Yoneda
embedding, and the notion of unitary adjunction for dagger functors between
2-Hilbert spaces.
