Inductive groupoids and normal categories of regular semigroups
Arangath Raghavan Rajan · 2018
Inductive groupoids and normal categories arise in the structure theory of regular semigroups. Inductive groupoid of a regular semigroup S is the groupoid G(S){(x, x ı ) : x ı is an inverse of x} which admits certain order structure. Normal category is an abstraction of the structure in the category of principal left [or right] ideals of a regular semigroup with translations as morphisms. Here we show that an inductive groupoid G(C) arises from every normal category C. In the case when S is a regular semigroup the inductive groupoids G(S) and G(C) where C is the normal category of principal left ideals of S are closely related.We provide explicit desciption of this relation