  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.
