2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/141062The definition of an S-category is proposed by weakening the axioms of a Q-category introduced by Kontsevich and Rosenberg. Examples of Q- and S-categories and (co)smooth objects in such categories are given.11 pagesRings and AlgebrasQuantum Algebra16W30; 18A40; 16D90text