2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154889We show that K_1 of an exact category agrees with K_1 of the associated triangulated derivator. More generally we show that K_1 of a Waldhausen category with cylinders and a saturated class of weak equivalences coincides with K_1 of the associated right pointed derivator.23 pages, the main results have been generalizedK-Theory and HomologyAlgebraic Topology18E10; 18E30; 18F25; 19B99; 55S45text