The geometric theory of inverse semigroups I: E-unitary inverse semigroups

M.V. Lawson
1990 Journal of Pure and Applied Algebra  
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 subsequent papers.
doi:10.1016/0022-4049(90)90011-6 fatcat:iebw67ziz5cw3anynxq2wdmwuy