2011/10/14 by Matthew Dyer, Dyer, Matthew
Computer Science · Decision Sciences · #06A12 #20F55 (Primary) 17B22 #20J99 (Secondary) #20L05 #Advanced Algebra and Logic #FOS: Mathematics #Fuzzy and Soft Set Theory #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1110.3217
openalex publication_date 2011/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first of a series of papers which define and study structures called rootoids, which are groupoids equipped with a representation in the category of Boolean rings and with an associated 1-cocycle. The axioms for rootoids are abstracted from formal properties of Coxeter groups with their root systems and weak orders. They imply that each of the weak orders of a rootoid embeds as an order ideal in a complete ortholattice. This first paper is concerned only with the most basic definitions, facts and examples; the main results, which are new even for Coxeter groups, will be stated and proved in subsequent papers. They involve certain categories of rootoids and especially a notion of functor rootoid.