Coherent presentations of structure monoids and the Higman-Thompson groups

Details Coherent presentations of structure monoids and the Higman-Thompson groups Coherent presentations of structure monoids and the Higman-Thompson groups

2008-02-24

arxiv.org/abs/0802.3511v1

Mathematics

Category Theory

22 pages

Scientific paper

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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