Endomorphism algebras of peak $I$-spaces over posets of infinite prinjective type

Abstract

We will derive a general result for $R$-categories which allows us to derive the existence of large objects with prescribed endomorphism algebras from the existence of small families. This theorem is based on an earlier result of S. Shelah in which he established the existence of indecomposable abelian groups of any cardinality. We will apply this ‘Shelah-elevator’ for abelian groups and - which is our main concern - for prescribing endomorphism algebras of peak $I$-spaces which are classified by a recent result of Simson.