nLab
n-angulated category

nn-angulated categories are a generalization to integers n3n\geq 3 of a triangulated category, which is obtained for n=3n = 3. They are introduced in

Its abstract reads:

We define nn-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-nn-angulations. We obtain a large class of examples of nn-angulated categories by considering (n2)(n-2)-cluster tilting subcategories of triangulated categories which are stable under the (n2)(n-2)nd power of the suspension functor. As an application, we show how nn-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

  • P.A. Bergh, M. Thaule, The axioms for nn-angulated categories, arXiv:1112.2533; The Grothendieck group of an nn-angulated category, arxiv/1205.5697

  • Gustavo Jasso, nn-abelian and nn-exact categories, arxiv/1405.7805

  • Zengqiang Lin, nn-angulated quotient categories induced by mutation pairs, arxiv/1409.2716

Revised on September 10, 2014 12:44:59 by Zoran Škoda (161.53.130.104)