ABSTRACT
Our main tool is a homological description of lim ,4 ,^. We show that in many cases the limit closure lim A of the first component in a cotorsion pair £ = (A, B] consists of all modules X satisfying Ext^(.X", B) — 0 for each pure-injective module B e B; there is also a characterization of lim A in terms of vanishing of Tor (see Section 2).
