-angulated categories are a generalization to integers of a triangulated category, which is obtained for . They are introduced in
Its abstract reads:
We define -angulated categories by modifying the axioms of triangulated categories in a natural way. We show that Heller’s parametrization of pre-triangulations extends to pre--angulations. We obtain a large class of examples of -angulated categories by considering -cluster tilting subcategories of triangulated categories which are stable under the nd power of the suspension functor. As an application, we show how -angulated Calabi-Yau categories yield triangulated Calabi-Yau categories of higher Calabi-Yau dimension. Finally, we sketch a link to algebraic geometry and string theory.
Other works are