A general construction of n-angulated categories using periodic injective resolutions

Abstract

Let C be an additive category equipped with an automorphism Σ. We show how to obtain n-angulations of (C,Σ) using some particular periodic injective resolutions. We give necessary and sufficient conditions on (C,Σ) admitting an n-angulation. Then we apply these characterizations to explain the standard construction of n-angulated categories and the n-angulated categories arising from some local rings. Moreover, we obtain a class of new examples of n-angulated categories from quasi-periodic selfinjective algebras.