On Parity Complexes and Non-abelian Cohomology
| dc.creator | Ionescu, Lucian M. | |
| dc.date | 1998-08-15 | |
| dc.date.accessioned | 2026-07-07T06:32:59Z | |
| dc.date.available | 2026-07-07T06:32:59Z | |
| dc.description | To characterize categorical constraints - associativity, commutativity and monoidality - in the context of quasimonoidal categories, from a cohomological point of view, we define the notion of a parity (quasi)complex. Applied to groups gives non-abelian cohomology. The categorification - functor from groups to monoidal categories - provides the correspondence between the respective parity (quasi)complexes and allows to interpret 1-cochains as functors, 2-cocycles - monoidal structures, 3-cocycles - associators. The cohomology spaces H3, H2, H1, H0 correspond as usual to quasi-extensions, extensions, split extensions and invariants, as in the abelian case. A larger class of commutativity constraints for monoidal categories is identified. It is naturally associated with coboundary Hopf algebras. | |
| dc.description | AMS-LaTex, 31 pages | |
| dc.identifier | https://arxiv.org/abs/math/9808068 | |
| dc.identifier | http://arxiv.org/abs/math/9808068 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/99045 | |
| dc.subject | Category Theory | |
| dc.subject | Group Theory | |
| dc.subject | 18D10 (Primary) 20J05, 18G50 (Secondary) | |
| dc.title | On Parity Complexes and Non-abelian Cohomology | |
| dc.type | text |