Nilpotent Category of Monoidal Category and Tensor–Hom Adjunction

IF 0.7 4区 数学 Q2 MATHEMATICS
Yan’en Ni, Yunfei Tan, Yunfei Yi, Yuehui Zhang
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引用次数: 0

Abstract

Let \(\mathcal {C}\) be an abelian monoidal category. It is proved that the nilpotent category \({\text {Nil}}(\mathcal {C})\) of \(\mathcal {C}\) admits almost monoidal structure except the unit axiom. As an application, it is proved that Hom and Tensor functors exist over \({\text {Nil}}(\mathcal {C})\) and tensor–hom adjunction remains true over the nilpotent category of the category of finite-dimensional vector spaces, which develops some recent results on this topic.

一元范畴的幂零范畴与张量-宏补
设\(\mathcal {C}\)是一个阿贝尔一元范畴。证明了\(\mathcal {C}\)的幂零范畴\({\text {Nil}}(\mathcal {C})\)除单位公理外,几乎允许单形结构。作为一个应用,证明了在\({\text {Nil}}(\mathcal {C})\)上存在宏函子和张量函子,并且在有限维向量空间范畴的幂零范畴上张量-宏共轭成立,从而发展了本课题的一些最新成果。
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来源期刊
Bulletin of The Iranian Mathematical Society
Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics
CiteScore
1.40
自引率
0.00%
发文量
64
期刊介绍: The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.
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