2011/10/17 by Matthew Dyer, Dyer, Matthew · 1 citation
Computer Science · #06A12 #20F05 (Secondary) #20F55 (Primary) 17B22 #20J99 #20L05 #Advanced Algebra and Logic #FOS: Mathematics #Group Theory (math.GR) #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1110.3657
openalex publication_date 2011/10/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the second introductory paper concerning structures called rootoids and protorootoids, the definition of which is abstracted from formal properties of Coxeter groups with their root systems and weak orders. The ubiquity of protorootoids is shown by attaching them to structures such as groupoids with generators, to simple graphs, to subsets of Boolean rings, to possibly infinite oriented matroids, and to groupoids with a specified preorder on each set of morphisms with fixed codomain; in each case, the condition that the structure give rise to a rootoid defines an interesting subclass of these structures. The paper also gives non-trivial examples of morphisms of rootoids and describes (without proof, and partly informally) some main ideas, results and questions from subsequent papers of the series, including the basic facts about principal rootoids and functor rootoids which together provide the raison d'être for these papers.