Cyclic structures for simplicial objects from comonads
| dc.creator | Skoda, Zoran | |
| dc.date | 2004-12-01 | |
| dc.date.accessioned | 2026-07-07T05:14:49Z | |
| dc.date.available | 2026-07-07T05:14:49Z | |
| dc.description | The simplicial endofunctor induced by a comonad in some category may underly a cyclic object in its category of endofunctors. The cyclic symmetry is then given by a sequence of natural transformations. We write down the commutation relations the first cyclic operator has to satisfy with the data of the comonad. If we add a version of quantum Yang Baxter relation and another relation we actually get a sufficient condition for constructing a sequence of higher cyclic operators in a canonical fashion. A degenerate case of this construction comes from so-called trivial symmetry of an additive comonad. We also consider weaker versions for paracyclic objects as well as some connections to the subject of distributive laws. | |
| dc.description | 18 pages; preliminary version | |
| dc.identifier | https://arxiv.org/abs/math/0412001 | |
| dc.identifier | http://arxiv.org/abs/math/0412001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/73430 | |
| dc.subject | Category Theory | |
| dc.subject | Quantum Algebra | |
| dc.subject | 19D55 | |
| dc.title | Cyclic structures for simplicial objects from comonads | |
| dc.type | text |