论文标题
类别和（部分）半群中理想的一致性晶格
Congruence lattices of ideals in categories and (partial) semigroups
论文作者
论文摘要
本文提出了一个统一的框架，用于确定转换，图表，矩阵和辫子以及所有理想的许多单体和类别的一致性。关键的理论进步提出了一个迭代过程，即在彼此之间将某些正常的亚组晶格堆叠在一起，以依次构建一系列理想链的一致性晶格。这适用于以下几个特定类别：转换；订单/定向保存/逆转转换；分区；平面/环形分区； Brauer，Tembyley- Lieb和Jones分区；线性和投影线性变换；和部分辫子。某些小型理想需要特殊考虑，并且在技术上对线性和部分编织类别的理论基础更为复杂。
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative process of stacking certain normal subgroup lattices on top of each other to successively build congruence lattices of a chain of ideals. This is applied to several specific categories of: transformations; order/orientation preserving/reversing transformations; partitions; planar/annular partitions; Brauer, Temperley--Lieb and Jones partitions; linear and projective linear transformations; and partial braids. Special considerations are needed for certain small ideals, and technically more intricate theoretical underpinnings for the linear and partial braid categories.
