论文标题
一类有序代数等效于多端gebras的类别
A Category of Ordered Algebras Equivalent to the Category of Multialgebras
论文作者
论文摘要
众所周知，集合与完整的原子布尔代数（CABA）之间有一个对应关系，将集合置于其功率集，并相互地，是完整的原子布尔代数到其一组原子元素。当然，这种对应关系诱导了$ \ textbf {set} $的相对类别与CABA的类别之间的等价性。我们通过将多零件在签名$σ$上取出，特别是那些非确定操作无法返回空定点的签名$σ$，并删除其零元素的CABA和与订单兼容的$σ$ -SELGEBRA的结构；相互，其中一个“几乎布尔” $σ$ -Algebras被带到其一组原子元素，该原子元素配备了超过$σ$的多级结构。这导致了$σ$ - 万格拉斯的类别与有序的$σ$ - 代理类别之间的等价性。在这里，直觉是，如果一个人希望这样做，那么非确定性可能会被基本结构的足够丰富的顺序取代。
It is well known that there is a correspondence between sets and complete, atomic Boolean algebras (CABA's) taking a set to its power-set and, reciprocally, a complete, atomic Boolean algebra to its set of atomic elements. Of course, such a correspondence induces an equivalence between the opposite category of $\textbf{Set}$ and the category of CABA's. We extend this result by taking multialgebras over a signature $Σ$, specifically those whose non-deterministic operations cannot return the empty-set, to CABA's with their zero element removed and a structure of $Σ$-algebra compatible with its order; reciprocally, one of these "almost Boolean" $Σ$-algebras is taken to its set of atomic elements equipped with a structure of multialgebra over $Σ$. This leads to an equivalence between the category of $Σ$-multialgebras and a category of ordered $Σ$-algebras. The intuition, here, is that if one wishes to do so, non-determinism may be replaced by a sufficiently rich ordering of the underlying structures.
