结构幺半群的相干表示与Higman-Thompson群
Coherent presentations of structure monoids and the Higman-Thompson groups
摘要：
结构幺半群和群是方程簇的代数不变式。我们将展示如何构建这些对象的演示文稿从连贯的equational品种，概括Dehornoy的几个结果。我们随后实现了更高的Thompson群$F_{n,1}$和Higman-Thompson群$G_{n,1}$作为结构群。我们继续通过高阶结合性和高阶结合性与交换性的各种相干的简化来得到这些群的表示。这些简化概括了Mac Lane的五边形和六边形条件的连贯关联和交换双函子。
英文摘要：
Structure monoids and groups are algebraic invariants of equational varieties. We show how to construct presentations of these objects from coherent categorifications of equational varieties, generalising several results of Dehornoy. We subsequently realise the higher Thompson groups $F_{n,1}$ and the Higman-Thompson groups $G_{n,1}$ as structure groups. We go on to obtain presentations of these groups via coherent categorifications of the varieties of higher-order associativity and of higher-order associativity and commutativity, respectively. These categorifications generalise Mac Lane's pentagon and hexagon conditions for coherently associative and commutative bifunctors.
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