论文标题
适当的Ehresmann半群
Proper Ehresmann semigroups
论文作者
论文摘要
我们基于对某些具有附加结构的标记的有向图控制的生成元素的三坐标描述，提出了适当的Ehresmann半群的概念。生成元素取决于其域投影，范围投影和$σ$ -Class，其中$σ$表示标识所有投影的最小一致性。我们证明了适当的Ehresmann Semigroups的结构，并表明每个Ehresmann Semigroup都有适当的掩护。从Branco，Gomes和Gould的工作中，我们的掩盖单层是同构的，并提供了后者的新视图。适当的ehresmann半群，所有元素都承认，三坐标描述的特征是在半层次上的单粒子的部分多构度。结果，我们在适当的限制半群中恢复了两坐标结构。
We propose a notion of a proper Ehresmann semigroup based on a three-coordinate description of its generating elements governed by certain labelled directed graphs with additional structure. The generating elements are determined by their domain projection, range projection and $σ$-class, where $σ$ denotes the minimum congruence that identifies all projections. We prove a structure result on proper Ehresmann semigroups and show that every Ehresmann semigroup has a proper cover. Our covering monoid turns out to be isomorphic to that from the work by Branco, Gomes and Gould and provides a new view of the latter. Proper Ehresmann semigroups all of whose elements admit a three-coordinate description are characterized in terms of partial multiactions of monoids on semilattices. As a consequence we recover the two-coordinate structure result on proper restriction semigroups.
