Exact categories, big Cohen-Macaulay modules and finite representation type

One of the first remarkable results in representation theory artin algebras, due to Auslander and Ringel-Tachikawa, is characterisation when an algebra representation-finite. In this paper, we investigate aspects representation-finiteness general context exact categories sense Quillen. framework, introduce “big objects” prove Auslander-type “splitting-big-objects” theorem. Our approach generalises unifies known from literature. As a further application our methods, extend theorems Ringel-Tachikawa arbitrary dimension, i.e. characterise Cohen-Macaulay order over complete regular local ring finite type.