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dc.contributor.authorStokes, Tim E.en_NZ
dc.date.accessioned2018-05-23T04:15:24Z
dc.date.available2017-04-01en_NZ
dc.date.available2018-05-23T04:15:24Z
dc.date.issued2017en_NZ
dc.identifier.citationStokes, T. E. (2017). D-semigroups and constellations. SEMIGROUP FORUM, 94(2), 442–462. https://doi.org/10.1007/s00233-017-9851-zen
dc.identifier.issn0037-1912en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/11858
dc.description.abstractIn a result generalising the Ehresmann–Schein–Nambooripad Theorem relating inverse semigroups to inductive groupoids, Lawson has shown that Ehresmann semigroups correspond to certain types of ordered (small) categories he calls Ehresmann categories. An important special case of this is the correspondence between two-sided restriction semigroups and what Lawson calls inductive categories. Gould and Hollings obtained a one-sided version of this last result, by establishing a similar correspondence between left restriction semigroups and certain ordered partial algebras they call inductive constellations (a general constellation is a one-sided generalisation of a category). We put this one-sided correspondence into a rather broader setting, at its most general involving left congruence D-semigroups (which need not satisfy any semiadequacy condition) and what we call co-restriction constellations, a finitely axiomatized class of partial algebras. There are ordered and unordered versions of our results. Two special cases have particular interest. One is that the class of left Ehresmann semigroups (the natural one-sided versions of Lawson’s Ehresmann semigroups) corresponds to the class of co-restriction constellations satisfying a suitable semiadequacy condition. The other is that the class of ordered left Ehresmann semigroups (which generalise left restriction semigroups and for which semigroups of binary relations equipped with domain operation and the inclusion order are important examples) corresponds to a class of ordered constellations defined by a straightforward weakening of the inductive constellation axioms.
dc.format.mimetypeapplication/pdf
dc.language.isoenen_NZ
dc.publisherSpringeren_NZ
dc.rightsThis is an author’s accepted version of an article published in the journal: Semigroup Forum. © Springer Science+Business Media New York 2017.
dc.subjectScience & Technologyen_NZ
dc.subjectPhysical Sciencesen_NZ
dc.subjectMathematicsen_NZ
dc.subjectD-semigroupen_NZ
dc.subjectLeft Ehresmann semigroupen_NZ
dc.subjectConstellationen_NZ
dc.subjectLEFT EHRESMANN MONOIDSen_NZ
dc.subjectLEFT ADEQUATEen_NZ
dc.titleD-semigroups and constellationsen_NZ
dc.typeJournal Article
dc.identifier.doi10.1007/s00233-017-9851-zen_NZ
dc.relation.isPartOfSEMIGROUP FORUMen_NZ
pubs.begin-page442
pubs.elements-id191971
pubs.end-page462
pubs.issue2en_NZ
pubs.publication-statusPublisheden_NZ
pubs.volume94en_NZ
dc.identifier.eissn1432-2137en_NZ


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