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dc.contributor.authorGould, Victoriaen_NZ
dc.contributor.authorStokes, Tim E.en_NZ
dc.date.accessioned2017-04-05T23:02:47Z
dc.date.available2017en_NZ
dc.date.available2017-04-05T23:02:47Z
dc.date.issued2017en_NZ
dc.identifier.citationGould, V., & Stokes, T. E. (2017). Constellations and their relationship with categories. Algebra Universalis, FirstView, 1–34. https://doi.org/10.1007/s00012-017-0432-5en
dc.identifier.issn0002-5240en_NZ
dc.identifier.urihttps://hdl.handle.net/10289/10980
dc.description.abstractConstellations are partial algebras that are one-sided generalisations of categories. Indeed, we show that a category is exactly a constellation that also satisfies the left-right dual axioms. Constellations have previously appeared in the context of inductive constellations: the category of inductive constellations is known to be isomorphic to the category of left restriction semigroups. Here we consider constellations in full generality, giving many examples. We characterise those small constellations that are isomorphic to constellations of partial functions. We examine in detail the relationship between constellations and categories. In particular, we characterise those constellations that arise as (sub-)reducts of categories. We demonstrate that the notion of substructure can be captured within constellations but not within categories. We show that every constellation P gives rise to a category (Formula presented.), its canonical extension, in a simplest possible way, and that P is a quotient of (Formula presented.) in a natural sense. We also show that many of the most common concrete categories may be constructed from simpler quotient constellations using this construction. We characterise the canonical congruences (Formula presented.) on a given category (Formula presented.) (those for which (Formula presented.), and show that the category of constellations is equivalent to the category of (Formula presented.)-categories, that is, categories equipped with distinguished canonical congruence (Formula presented.). The main observation of this paper is that category theory as it applies to the familiar concrete categories of modern mathematics (which come equipped with natural notions of substructures and indeed are (Formula presented.)-categories) may be subsumed by constellation theory.en_NZ
dc.format.mimetypeapplication/pdf
dc.language.isoen
dc.publisherSpringeren_NZ
dc.rightsThis is an author’s submitted version of an article published in the journal: Algebra Universalis. © Springer International Publishing 2017. The final publication is available at Springer via dx.doi.org/10.1007/s00012-017-0432-5
dc.subjectmathematicsen_NZ
dc.subjectconstellationen_NZ
dc.subjectcategoryen_NZ
dc.subjectpartial algebraen_NZ
dc.titleConstellations and their relationship with categoriesen_NZ
dc.typeJournal Article
dc.identifier.doi10.1007/s00012-017-0432-5en_NZ
dc.relation.isPartOfAlgebra Universalisen_NZ
pubs.begin-page1
pubs.elements-id192518
pubs.end-page34
pubs.organisational-group/Waikato
pubs.organisational-group/Waikato/2018 PBRF
pubs.organisational-group/Waikato/FCMS
pubs.organisational-group/Waikato/FCMS/2018 PBRF - FCMS
pubs.publication-statusAccepteden_NZ
pubs.volumeFirstViewen_NZ


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