N-spherical functors and tensor categories

Recently, Dyckerhoff, Kapranov and Schechtman introduced a notion of N-spherical functors of stable infinity categories, generalising the notion of spherical functors (as studied by Anno, Kuznetsov and others).
We apply this to the setting of tensor categories; calling an object N-bounded if the corresponding regular endofunctor on the derived category is N-spherical. Besides giving new examples of N-spherical functors, the notion of N-bounded objects gives surprising connections with Jones-Wenzl idempotents, Frobenius-Perron dimensions and the main conjectures in the field of tensor categories.
Based on joint work with Pavel Etingof.