The Auslander–Reiten correspondence for n-F-tilting pairs

The Auslander–Reiten correspondence is a gem of great interest in tilting theory. Let [Formula: see text] be an additive subfunctor of [Formula: see text], and let [Formula: see text] be an Artin [Formula: see text]-algebra. We apply similar methods to tilting pairs to study [Formula: see text]-tilting pairs in [Formula: see text]-mod. A relative Auslander–Reiten type correspondence between the class of basic [Formula: see text]-[Formula: see text]-[Formula: see text]-tilting modules (with respect to an [Formula: see text]-[Formula: see text]-tilting pair [Formula: see text]) and certain covariantly finite subcategories is established. This result extends the Auslander–Reiten correspondence previously established by Wei Auslander–Reiten correspondence for tilting pairs, J. Pure Appl. Algebra 212(2) (2008) 411–422.