$n$-angulated categories

TL;DR

This paper introduces $n$-angulated categories as a generalization of triangulated categories, extending existing axioms and providing new examples, with applications to Calabi-Yau categories and potential links to algebraic geometry and string theory.

Contribution

It defines $n$-angulated categories, extends Heller's parametrization, constructs examples via cluster tilting subcategories, and explores applications to Calabi-Yau categories and theoretical physics.

Findings

Defined $n$-angulated categories by modifying triangulated axioms.

Extended Heller's parametrization to pre-$n$-angulations.

Provided examples using $(n-2)$-cluster tilting subcategories.

Abstract

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