$n$-angulated categories
K-Theory and Homology
2019-07-15 v4 Rings and Algebras
Representation Theory
Abstract
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.
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