Mittag-Leffler conditions and projectively coresolved Gorenstein flat tilting modules

We first make an approach to the Mittag-Leffler condition in the theory of relative Ext-orthogonal classes and establish the balance of the relative derived functors of the Hom and tensor product functors with respect to the classes of projectively coresolved Gorenstein flat modules and Gorenstein injective modules. Then, we introduce the concepts of PGF-tilting modules and PGF-weak tilting modules. By means of Mittag-Leffler conditions, we explore the connection between PGF-tilting modules and PGF-weak tilting modules. As an application, we study when Gorenstein tilting modules are Gorenstein weak tilting.