Relative tilting pairs

Abstract

Let $\Lambda$ 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 $\mathrm{Ext}_{\Lambda}^1(-,~-)$. 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.

Keywords

• Tilting module
• $F$-orthogonal class
• $r\textrm{-}F$-tilting pair

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