On Parity Complexes and Non-abelian Cohomology

dc.creatorIonescu, Lucian M.
dc.date1998-08-15
dc.date.accessioned2026-07-07T06:32:59Z
dc.date.available2026-07-07T06:32:59Z
dc.descriptionTo 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.descriptionAMS-LaTex, 31 pages
dc.identifierhttps://arxiv.org/abs/math/9808068
dc.identifierhttp://arxiv.org/abs/math/9808068
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/99045
dc.subjectCategory Theory
dc.subjectGroup Theory
dc.subject18D10 (Primary) 20J05, 18G50 (Secondary)
dc.titleOn Parity Complexes and Non-abelian Cohomology
dc.typetext

Files

Collections