Pre-(n + 2)-angulated categories
| Autor: | He, Jing, Zhou, Panyue, Zhou, Xingjia |
|---|---|
| Rok vydání: | 2023 |
| Předmět: |
Mathematics::Functional Analysis
Algebra and Number Theory Mathematics::K-Theory and Homology Mathematics::Category Theory FOS: Mathematics Mathematics::General Topology Category Theory (math.CT) Mathematics - Category Theory Representation Theory (math.RT) Mathematics::Representation Theory Mathematics - Representation Theory |
| Zdroj: | Journal of Algebra. 620:452-477 |
| ISSN: | 0021-8693 |
| Popis: | In this article, we introduce the notion of pre-$(n+2)$-angulated categories as higher dimensional analogues of pre-triangulated categories defined by Beligiannis-Reiten. We first show that the idempotent completion of a pre-$(n+2)$-angulated category admits a unique structure of pre-$(n+2)$-angulated category. Let $(\mathscr{C},\mathbb{E},\mathfrak{s})$ be an $n$-exangulated category and $\mathscr{X}$ be a strongly functorially finite subcategory of $\mathscr{C}$. We then show that the quotient category $\mathscr{C}/\mathscr{X}$ is a pre-$(n+2)$-angulated category.These results allow to construct several examples of pre-$(n+2)$-angulated categories. Moreover, we also give a necessary and sufficient condition for the quotient $\mathscr{C}/\mathscr{X}$ to be an $(n+2)$-angulated category. 20 pages. arXiv admin note: text overlap with arXiv:2108.07985, arXiv:2006.02223 |
| Databáze: | OpenAIRE |
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