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arXiv · 1006.4592

$n$-angulated categories

Christof Geiss·Bernhard Keller·Steffen Oppermann
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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.

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Christof Geiss, Bernhard Keller, Steffen Oppermann. 2010-06-23. $n$-angulated categories. https://doi.org/10.1515/crelle.2011.177

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