Duplicial sets, crossed $G$-sets and descent categories
Quantum Algebra
2026-05-27 v1
Abstract
The goal of this note is to show that the left -coalgebra, which is an additional structure on one of the coefficients used in the construction of the cyclic operator for the cyclic sets that generalises the twisted nerve of a group by Loday is an instance of a general theory of left -coalgebras. It is also shown that in the general case, the resulting cyclic operator requires that the other coefficient needs to be equipped with a crossed -sets structure.
Cite
@article{arxiv.2605.27092,
title = {Duplicial sets, crossed $G$-sets and descent categories},
author = {John Boiquaye and Ralph Twum},
journal= {arXiv preprint arXiv:2605.27092},
year = {2026}
}