论文标题
来自（CO）HOPF辅助的Frobenius Monoidal函子
Frobenius monoidal functors from (co)Hopf adjunctions
论文作者
论文摘要
令$ u：\ mathcal {c} \ rightArrow \ Mathcal {d} $是Abelian Monoidal类别之间强大的单型函数，承认右伴随$ r $，因此$ r $是确切的，忠实的，忠实的，aDjuntuntion $ u \ u \ u \ dashv r $是cohopf。在Balan的作品的基础上，我们表明$ r $可分开（special）frobenius hionoidal，并且仅当$ r（\ mathbb {1} _ {\ mathcal {d}}）$是可分离的（special，special）frobenius algebra in $ \ \ m m iathcal {c c} $。如果更进一步，$ \ nathcal {c}，\ Mathcal {d} $是关键（分别，功能区）类别，$ u $是一个关键（resp。，编织的枢纽）函数，那么$ r $是一个关键（resp。，ribbon）函数，当时仅在当时，当时，当$ r（\ mathbb {1} _ {\ Mathcal {d}}）$是$ \ Mathcal {C} $中的对称的Frobenius algebra。作为一个应用程序，我们构造了进入Drinfeld中心$ \ MATHCAL {Z}（\ Mathcal {C}）$的Frobenius Monoidal函数，从而在其中产生了Frobenius代数。
Let $U:\mathcal{C}\rightarrow\mathcal{D}$ be a strong monoidal functor between abelian monoidal categories admitting a right adjoint $R$, such that $R$ is exact, faithful and the adjunction $U\dashv R$ is coHopf. Building on the work of Balan, we show that $R$ is separable (resp., special) Frobenius monoidal if and only if $R(\mathbb{1}_{\mathcal{D}})$ is a separable (resp., special) Frobenius algebra in $\mathcal{C}$. If further, $\mathcal{C},\mathcal{D}$ are pivotal (resp., ribbon) categories and $U$ is a pivotal (resp., braided pivotal) functor, then $R$ is a pivotal (resp., ribbon) functor if and only if $R(\mathbb{1}_{\mathcal{D}})$ is a symmetric Frobenius algebra in $\mathcal{C}$. As an application, we construct Frobenius monoidal functors going into the Drinfeld center $\mathcal{Z}(\mathcal{C})$, thereby producing Frobenius algebras in it.
