Groupoids, root systems and weak order I [article]

Matthew Dyer
2011 arXiv   pre-print
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
more » ... ns, 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.
arXiv:1110.3217v1 fatcat:wmr3to6lljfubomsx3lv43f27y