We describe the universal target of annular Khovanov-Rozansky link homology
functors as the homotopy category of a free symmetric monoidal category
generated by one object and one endomorphism. This categorifies the ring of
symmetric functions and admits categorical analogues of plethystic
transformations, which we use to characterize the annular invariants of Coxeter
braids. Further, we prove the existence of symmetric group actions on the
Khovanov-Rozansky invariants of cabled tangles and we introduce spectral
sequences that aid in computing the homologies of generalized Hopf links.
Finally, we conjecture a characterization of the horizontal traces of Rouquier
complexes of Coxeter braids in other types.Comment: 41 page
