Generalized Koszul properties for augmented algebras

Under certain conditions, a filtration on an augmented algebra A admits a related filtration on the Yoneda algebra E(A):=ExtA(K,K). We show that there exists a bigraded algebra monomorphism , where EGr(grA) is the graded Yoneda algebra of grA. This monomorphism can be applied in the case where A is connected graded to determine that A has the K2 property recently introduced by Cassidy and Shelton.