Let R be a ring and consider the category ModR of (right) R-modules. Given a class C ofR-modules, a morphismM → N in ModR is called a left C-approximation of M provided that N belongs to C and the induced morphism HomR(N,C) → HomR(M,C) is surjective for every C in C. This concept has been introduced by Auslander and Smalø [2], and independently by Enochs [5]. Approximations arise naturally in v...
