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.

中文翻译：

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幺半群范畴的幂零范畴和张量-Hom 附加

令\(\mathcal {C}\)为阿贝尔幺半群范畴。证明了\(\mathcal {C}\)的幂零范畴\({\text {Nil}}(\mathcal {C}) \ )除了单位公理外几乎承认幺半群结构。作为应用，证明了 Hom 和张量函子在\({\text {Nil}}(\mathcal {C})\)上存在，并且张量-hom 附加在有限维范畴的幂零范畴上仍然成立。向量空间，它开发了有关该主题的一些最新结果。