2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69794To any left system of diagram categories or to any left pointed derivateur (in the sense of Grothendieck) a K-theory space is associated. This K-theory space is shown to be canonically an infinite loop space and to have a lot of common properties with Waldhausen's K-theory. A weaker version of additivity is shown. Also, Quillen's K-theory of a large class of exact categories including the abelian categories is proved to be a retract of the K-theory of the associated derivateur.50 pagesK-Theory and HomologyCategory Theory19D99text