English

$n$-angulated categories

K-Theory and Homology 2019-07-15 v4 Rings and Algebras Representation Theory

Abstract

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.

Keywords

Cite

@article{arxiv.1006.4592,
  title  = {$n$-angulated categories},
  author = {Christof Geiss and Bernhard Keller and Steffen Oppermann},
  journal= {arXiv preprint arXiv:1006.4592},
  year   = {2019}
}

Comments

notation in axiom F2 clarified, 16 pages; v3: new section 5.5, minor corrections, to appear in Crelle's Journal; v4: published version

R2 v1 2026-06-21T15:40:08.529Z