2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/128609We investigate when Isomorphism Conjectures, such as the ones due to Baum-Connes, Bost and Farrell-Jones, are stable under colimits of groups over directed sets (with not necessarily injective structure maps). We show in particular that both the K-theoretic Farrell-Jones Conjecture and the Bost Conjecture with coefficients hold for those groups for which Higson, Lafforgue and Skandalis have disproved the Baum-Connes Conjecture with coefficients.30 pages This is the final version, minor changes only. It will appear in the Valladolid Conference on K-theory and Noncommutative GeometryK-Theory and Homology19K99, 18F25, 55N91text