Cyclic duality for slice and orbit 2-categories

Abstract

The self-duality of the paracyclic category is extended to a certain class of homotopy categories of (2,1)-categories. These generalise the orbit category of a group and are associated to certain self-dual preorders equipped with a presheaf of groups and a cosieve. Slice 2-categories of equidimensional submanifolds of a compact manifold without boundary form a particular case, and for $S^1$, one recovers cyclic duality. This provides in particular a visualisation of the results of B\"ohm and \c{S}tefan on the topic.