On F-almost split sequences

Let Λ be an Artinian algebra and F an additive subbifunctor of Ext_Λ¹(−,−) having enough projectives and injectives. We prove that the dualizing subvarieties of mod Λ closed under F-extensions have F-almost split sequences. Let T be an F-cotilting module in mod Λ and S a cotilting module over Γ = End(T). Then Hom(−, T) induces a duality between F-almost split sequences in ^⊥F T and almost split sequences in ^⊥ S, where add_Γ S = Hom_Λ( $ A \cong \Omega _{CM_F }^{ - d} D\Omega _{F^{op} }^{ - d} TRC \cong \Omega _{CM_F }^{ - d} \Omega _F^d DTrC $ A \cong \Omega _{CM_F }^{ - d} D\Omega _{F^{op} }^{ - d} TRC \cong \Omega _{CM_F }^{ - d} \Omega _F^d DTrC .