On extensions of abelian categories with applications to ring theory (Q1312862)

The author defines the \(\eta\)-extension \(D(\eta)\) of an abelian category \(D\) by the natural transformation \(\eta\colon F^ 2 \overset \circ\rightarrow F\) where \(F\colon D\to D\) is a covariant additive right exact functor, and discusses the relations between special objects in \(D\) and \(D(\eta)\) (e.g., projective, injective, etc. objects). By specializing the results to module categories one obtains a framework for well-known ring extensions. Furthermore, in propostion 5.6 the author computes the group \(\text{Ext}^ 1\) between any two simple modules \(X\), \(T\) of the ring \(D(M,\eta)\) where \(D\) is a semiperfect ring.