A generalized Koszul theory and its relation to the classical theory

Let A=⨁i⩾0AiA=⨁i⩾0Ai be a graded locally finite k  -algebra where A0A0 is a finite dimensional algebra whose finitistic dimension is 0. In this paper we develop a generalized Koszul theory preserving many classical results, and show an explicit correspondence between this generalized theory and the classical theory. Applications in representations of certain categories and extension algebras of standard modules of standardly stratified algebras are described.