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FACTORIZATION THEOREMS FOR MORPHISMS OF ORDERED GROUPOIDS AND INVERSE SEMIGROUPS

Published online by Cambridge University Press:  20 January 2009

Benjamin Steinberg
Benjamin Steinberg
Affiliation:
Faculdade de Ciências, da Universidade do Porto, 4099-002 Porto, Portugal ([email protected])
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Abstract

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Adapting the theory of the derived category to ordered groupoids, we prove that every ordered functor (and thus every inverse and regular semigroup homomorphism) factors as an enlargement followed by an ordered fibration. As an application, we obtain Lawson’s version of Ehresmann’s Maximum Enlargement Theorem, from which can be deduced the classical theory of idempotent-pure inverse semigroup homomorphisms and $E$-unitary inverse semigroups.

AMS 2000 Mathematics subject classification: Primary 20M18; 20L05; 20M17

Keywords

ordered groupoidsgroupoidssemidirect productsinverse semigroupsfibrationsderived categories
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 44 , Issue 3 , October 2001 , pp. 549 - 569
Copyright
Copyright © Edinburgh Mathematical Society 2001