  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'\^etre for
these papers.
