Let be an artin algebra. We extend Miyashita's theory of tilting pairs to the setting of relative tilting pairs with respect to an additive subfunctor F of Ext_¹ (-, ~-). Building on Wei's work on Miyashita's ordinary tilting pairs, we establish an equivalent characterization for relative tilting pairs, which provides a unified framework that generalizes several important results in tilting theory, including classical tilting pairs, F-tilting modules, and Gorenstein tilting pairs.
Wang et al. (Wed,) studied this question.