Well Generatedness and Adjoints for Homotopy Categories of N-complexes

Abstract

Let R be a ring and N ≥ 2. First, we prove that any deconstructible class of modules F over R induces two coreflective subcategories of the homotopy category KN (Mod−R) of (unbounded) N -complexes of right R-modules: the one whose objects are all N - complexes with components in F, KN (F), and the one whose objects are the N - acyclic complexes with components in F, AN (F). Second, we prove that for any decomposable class of modules G, the homotopy category of N -complexes, KN (G), is well generated. In particular, the homotopy category of N -complexes of projective modules is ℵ1 -generated, which extends the well known result of Neeman for N = 2.