  We generalize Jones' planar algebras by internalising the notion to a pivotal
braided tensor category $\mathcal{C}$. To formulate the notion, the planar
tangles are now equipped with additional `anchor lines' which connect the inner
circles to the outer circle. We call the resulting notion an anchored planar
algebra. If we restrict to the case when $\mathcal{C}$ is the category of
vector spaces, then we recover the usual notion of a planar algebra. Building
on our previous work on categorified traces, we prove that there is an
equivalence of categories between anchored planar algebras in $\mathcal{C}$ and
pivotal module tensor categories over $\mathcal{C}$ equipped with a chosen
self-dual generator. Even in the case of usual planar algebras, the precise
formulation of this theorem, as an equivalence of categories, has not appeared
in the literature. Using our theorem, we describe many examples of anchored
planar algebras.
