A classification of algebras stratified for all preorders by Koszul theory

Let $A = \bigoplus_{i \geqslant 0} A_i$ be a graded locally finite $k$-algebra such that $A_0$ is an arbitrary finite-dimensional algebra satisfying some splitting condition. In this paper we develop a generalized Koszul theory generalizing many classical results, and use it to classify algebras stratified for all preorders.