Planar algebras in braided tensor categories

Understand

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.