Auslander–Reiten correspondence for tilting pairs

Let A be an Artin algebra. A pair (C,T) of A-modules is tilting provided that C and T are (finitely generated) self-orthogonal, image and image. Particularly, T is a tilting module if and only if (A,T) is a tilting pair. In the note, we will extend the Auslander–Reiten correspondence for tilting modules to the context of tilting pairs.