Cyclic duality for slice and orbit 2-categories
Category Theory
2022-02-28 v1 K-Theory and Homology
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 , one recovers cyclic duality. This provides in particular a visualisation of the results of B\"ohm and \c{S}tefan on the topic.
Cite
@article{arxiv.2202.12772,
title = {Cyclic duality for slice and orbit 2-categories},
author = {John Boiquaye and Philipp Joram and Ulrich Krähmer},
journal= {arXiv preprint arXiv:2202.12772},
year = {2022}
}