论文标题
Nakayama funcor for Monads在有限的Abelian类别上
Nakayama functor for monads on finite abelian categories
论文作者
论文摘要
如果$ \ MATHCAL {M} $是有限的Abelian类别，并且$ \ Mathbf {T} $是$ \ Mathcal {M} $上的线性正确的单元，则类别$ \ Mathbf {t} \ mbox {t} \ mbox {-mod} $ of $ \ mathbf {-mmod} $ of $ \ mathbf {t} $ modiite is inite is inite is in IS fiter is a in IS fit is a。在假设Monad $ \ Mathbf {t} $的基础函数的假设下，我们给出了$ \ mathbf {t} \ mbox {-mod} $的Nakayama函数的明确公式。作为应用程序，我们推断出有限双模型类别中心中心函子的公式和有限张量类别的偶。还讨论了HOPF代数理论的一些示例。
If $\mathcal{M}$ is a finite abelian category and $\mathbf{T}$ is a linear right exact monad on $\mathcal{M}$, then the category $\mathbf{T}\mbox{-mod}$ of $\mathbf{T}$-modules is a finite abelian category. We give an explicit formula of the Nakayama functor of $\mathbf{T}\mbox{-mod}$ under the assumption that the underlying functor of the monad $\mathbf{T}$ has a double left adjoint and a double right adjoint. As applications, we deduce formulas of the Nakayama functor of the center of a finite bimodule category and the dual of a finite tensor category. Some examples from the Hopf algebra theory are also discussed.
