Dévissage and localization for the Grothendieck spectrum of varieties

We introduce a new perspective on the K-theory of exact categories via notion CGW-category. CGW-categories are generalization that admit Quillen Q-construction, but which also include examples such as finite sets and varieties. By analyzing Quillen's proofs dévissage localization we define ACGW-categories, an analogous abelian for prove theorems akin to localization. In particular, although category varieties is not quite ACGW, reduced schemes type is; applying allows us calculate filtration type. As application this theory construct comparison map showing two authors' definitions Grothendieck spectrum equivalent.