Abstract
Let [Formula: see text] be an [Formula: see text]-finite, Krull–Schmidt and [Formula: see text]-linear [Formula: see text]-exangulated category with [Formula: see text] a commutative artinian ring. In this note, we prove that [Formula: see text] has Auslander–Reiten–Serre duality if and only if [Formula: see text] has Auslander–Reiten [Formula: see text]-exangles. Moreover, we also give an equivalent condition for the existence of Serre duality (which is a special type of Auslander–Reiten–Serre duality). Finally, assume further that [Formula: see text] has Auslander–Reiten–Serre duality. We exploit a bijection triangle, which involves the restricted Auslander bijection and the Auslander–Reiten–Serre duality.
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