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 (Formula presented.) 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, (Formula presented.) and (Formula presented.) As a result, it will be shown that, in this case, (Formula presented.) admits a Serre functor and hence has Auslander–Reiten triangles. © 2018, © 2018 Taylor & Francis.