n－外角范畴的泛扩张

Universal extensions in n－exangulated categories

摘要

假设 ($\mathscr{C}$,E,s) 是n－外角范畴，给出半泛扩张和泛扩张的定义，证明$\mathscr{C}$中半泛扩张总是存在的，对于泛扩张的存在性给出一个充分必要条件，推广外部三角范畴中的相关结论。

Abstract

Let ($\mathscr{C}$,E,s) be an n-exangulated category．The notions of semi-universal extensions and universal extensions are intro- duced．It is shown that semi-universal extensions always exist．A necessary and sufficient condition of the existence of universal extensions is given．The results generalize some conclusions in extriangulated categories．

关键词

n－外角范畴 / 半泛扩张 / 泛扩张 / 投射盖

Key words

n-exangulated category / semi-universal extension / universal extension / projective cover

参考文献

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基金资助

甘肃省青年科技基金资助项目(23JRRA825)

湖南省教育厅科学研究项目优秀青年基金资助项目(24B0573)

湖南省教育厅科学研究项目重点资助项目(24A0221)

国家自然科学基金资助项目(12401045)