The N-stable category

A well-known theorem of Buchweitz provides equivalences between three categories: the stable category of Gorenstein projective modules over a Gorenstein algebra, the homotopy category of acyclic complexes of projectives, and the singularity category. To adapt this result to N -complexes, one must find an appropriate candidate for the N -analogue of the stable category. We identify this “ N -stable category” via the monomorphism category and prove Buchweitz’s theorem for N -complexes over a Grothendieck abelian category. We also compute the Serre functor on the N -stable category over a self-injective algebra and study the resultant fractional Calabi–Yau properties.