Duality and Serre functor in homotopy categories
ABSTRACT For a (right and left) coherent ring A, we show that there exists a duality between homotopy categories and 𝕂b(mod-A). If A = Λ is an artin algebra of finite global dimension, this duality induces a duality between their subcategories of acyclic complexes, and As a result, it will be shown that, in this case, admits a Serre functor and hence has Auslander–Reiten triangles.