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arXiv · 1709.06689

$n$-exangulated categories

Martin Herschend·Yu Liu·Hiroyuki Nakaoka
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Abstract

For each positive integer $n$ we introduce the notion of $n$-exangulated categories as higher dimensional analogues of extriangulated categories defined by Nakaoka-Palu. We characterize which $n$-exangulated categories are $n$-exact in the sense of Jasso and which are $(n+2)$-angulated in the sense of Geiss-Keller-Oppermann. For extriangulated categories with enough projectives and injectives we introduce the notion of $n$-cluster tilting subcategories and show that under certain conditions such $n$-cluster tilting subcategories are $n$-exangulated.

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Martin Herschend, Yu Liu, Hiroyuki Nakaoka. 2017-09-20. $n$-exangulated categories. https://arxiv.org/abs/1709.06689

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