A categorical genealogy for the congruence distributive property.
An alternative (tree-based) semantics for a class of regular expressions is proposed that assigns a central rôle to the + operator and thus to nondeterminism and nondeterministic choice. For the new semantics a consistent and complete axiomatization is obtained from the original axiomatization of regular expressions by Salomaa and by Kozen by dropping the idempotence law for + and the distribution law of • over +.
The paper contains two remarks on finite sets of groupoid terms closed under subterms and the application of unifying pairs.
It is shown that every concretizable category can be fully embedded into the category of accessible set functors and natural transformations.