2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/136644We explain how, under some hypotheses, one can construct a sequence of finite dimensional $kG$-modules that lie in certain prescribed additive subcategories, but whose direct limits do not. We use these to show that many of the triangulated quotients of $\Mod$ are not generated, as triangulated categories, by the corresponding quotient of $\mod$ considered as a full subcategory.5 pages, expanding on a construction from the author's PhD thesisRepresentation Theory16G60, 18A30, 18Exx, 18G25, 20C05, 20C20text