AbstractLet R be a left coherent ring, S a right coherent ring and RU a generalized tilting module, with S=End(RU) satisfying the condition that each finitely presented left R-module X with ExtRi(X,U)=0 for any i≥1 is U-torsionless. If M is a finitely presented left R-module such that ExtRi(M,U)=0 for any i≥0 with $i \neq n$ (where n is a nonnegative integer), then $\mathrm {Ext}_S^n( \mathrm {Ext}_R^n(M, U), U)\cong M$ and ExtSi(ExtRn(M,U),U)=0 for any i≥0 with $i\neq n$. A duality is thus induced between the category of finitely presented holonomic left R-modules and the category of finitely presented holonomic right S-modules.