论文标题
连续函数环上的越野函数和模态运算符
The Vietoris functor and modal operators on rings of continuous functions
论文作者
论文摘要
我们在类别上引入了一个$ h $的$ h $，$ h $ $ bal $的Archimedean $ \ ell $ -Algebras，并表明类别$ alg（h）$ h $ for $ h $的代数与coalg（v）类别的coalgeberas的calgebras for vietoris endofunctor $ v $ v $ v $ concactor的coalgeberas castector的cargge（h）$ v $ v $ v $ v $ concactor的类别。我们还在$ bal $均匀完整的对象组成的$ bal $的反射子类别上引入了一个endofunctor $ hu $，并表明Gelfand Duality Liftity升至$ ALG（HU）$和$ COALG（v）$之间的双重等价。一方面，这概括了\ cite {abr88，kkv04}的结果，对于越野孔的结构类别类别，在石材空间的类别上。另一方面，它产生了\ cite {bcm20a}的最新结果的替代证明。
We introduce an endofunctor $H$ on the category $bal$ of bounded archimedean $\ell$-algebras and show that there is a dual adjunction between the category $Alg(H)$ of algebras for $H$ and the category $Coalg(V)$ of coalgebras for the Vietoris endofunctor $V$ on the category of compact Hausdorff spaces. We also introduce an endofunctor $Hu$ on the reflective subcategory of $bal$ consisting of uniformly complete objects of $bal$ and show that Gelfand duality lifts to a dual equivalence between $Alg(Hu)$ and $Coalg(V)$. On the one hand, this generalizes a result of \cite{Abr88,KKV04} for the category of coalgebras of the Vietoris endofunctor on the category of Stone spaces. On the other hand, it yields an alternate proof of a recent result of \cite{BCM20a}.
