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.
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Communicated by Rasool Hafezi.
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Supported by the NSF of China (11671258 and 11771280), and NSF of Shanghai (17ZR1415400).
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Ni, Y., Tan, Y., Yi, Y. et al. Nilpotent Category of Monoidal Category and Tensor–Hom Adjunction. Bull. Iran. Math. Soc. 49, 86 (2023). https://doi.org/10.1007/s41980-023-00831-2
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DOI: https://doi.org/10.1007/s41980-023-00831-2