Generalized logic and the representation of rings

Simon Ambler, Dominic Verity

    Research output: Contribution to journalArticleResearchpeer-review

    Abstract

    Following the progression towards weaker logics, a number of authors have considered the notion of a 'sheaf over a quantale' or, equivalently, a 'quantale valued set'. In this paper, we use ideas from enriched category theory to motivate the definition of a 'quantic sheaf'. Given a localic subquantale of Q, a quantic sheaf over Q gives a sheaf in the usual sense. As an application, we derive a series of sheaf representations for commutative rings including the familiar Pierce representation.

    LanguageEnglish
    Pages283-296
    Number of pages14
    JournalApplied Categorical Structures
    Volume4
    Issue number2-3
    Publication statusPublished - 1996

    Fingerprint

    Sheaves
    Logic
    Ring
    Quantale
    Enriched Category
    Category Theory
    Progression
    Commutative Ring
    Series

    Keywords

    • Enriched category
    • Quantale
    • Quantic sheaf
    • Ring representation

    Cite this

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    Generalized logic and the representation of rings. / Ambler, Simon; Verity, Dominic.

    In: Applied Categorical Structures, Vol. 4, No. 2-3, 1996, p. 283-296.

    Research output: Contribution to journalArticleResearchpeer-review

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