U.W. Bangor - School of Informatics - Mathematics Preprints 1992
Semigroup and Automata Theory
92.07 : LAWSON, M.V.
The geometric theory of inverse semigroups
I: E-unitary inverse semigroups
We show how the correspondence between inverse semigroups and
inductive groupoids ( a class of ordered groupoids)
leads to a reinterpretation of McAlister's P-Theorem
as a function extension theorem.
This result can only be expressed, in general,
by working within a larger category:
namely that of functorially ordered groupoids.
The consequences of this approach for the theory of E-unitary covers
of inverse semigroups and its generalisations are worked out in
J. Pure Appl. Algebra, 67 (1990) 151-177.