论文标题
Ehresmann理论和分区单型
Ehresmann theory and partition monoids
论文作者
论文摘要
本文涉及分区中的Ehresmann结构honoid $ p_x $。由于$ p_x $包含同一基础集合$ x $上的对称和双对称性逆，因此自然包含两个下monoids的同志的半武器。我们表明，其中一个半层次导致$ p_x $的Ehresmann结构，而另一个则没有。我们探讨了这一点（结构/组合和表示理论）的一些后果，尤其是左，右和两侧限制性下monoi类型。新的结果与已知的结果相关的关系形成鲜明对比，并且出现了许多有趣的二元性，这是源于反向半群的传统哲学作为部分对称的模型（Vagner和Preston）的模型（Vagner和Preston）或阻止对称性（Fitzgerald和Leech）：“子集之间的冲突”对关系之间的相互作用”。我们还考虑了一些相关的图表单体，包括rok分区单杆，并陈述了几个开放问题。
This article concerns Ehresmann structures in the partition monoid $P_X$. Since $P_X$ contains the symmetric and dual symmetric inverse monoids on the same base set $X$, it naturally contains the semilattices of idempotents of both submonoids. We show that one of these semilattices leads to an Ehresmann structure on $P_X$ while the other does not. We explore some consequences of this (structural/combinatorial and representation theoretic), and in particular characterise the largest left-, right- and two-sided restriction submonoids. The new results are contrasted with known results concerning relation monoids, and a number of interesting dualities arise, stemming from the traditional philosophies of inverse semigroups as models of partial symmetries (Vagner and Preston) or block symmetries (FitzGerald and Leech): "surjections between subsets" for relations become "injections between quotients" for partitions. We also consider some related diagram monoids, including rook partition monoids, and state several open problems.
