Let \(\varvec{G}\) (resp. \(\varvec{H}\) ) be the group of orientation preserving self-homeomorphisms of the unit circle (resp. real line). In previous work, the first two authors constructed pre-Tannakian categories and associated to these groups. In the predecessor to this paper, we analyzed the category (which we named the “Delannoy category”) in great detail, and found it to have many special properties. In this paper, we study . The primary difference between these two categories is that is semi-simple, while is not; this introduces new complications in the present case. We find that is closely related to the combinatorics of objects we call Delannoy loops, which seem to have not previously been studied.
