2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/146019We study some classes of lazy cocycles, called pure (respectively neat), together with their categorical counterparts, entwined (respectively strongly entwined) monoidal categories.Final version; 18 pages; the title has been changed; the order of the sections has been changed; some things have been removed and appear now in arXiv:0801.2055Quantum AlgebraOn some classes of lazy cocycles and categorical structurestext