Generalized logic and the representation of rings

Simon Ambler*, Dominic Verity

*Corresponding author for this work

    Research output: Contribution to journalArticle

    3 Citations (Scopus)

    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.

    Original languageEnglish
    Pages (from-to)283-296
    Number of pages14
    JournalApplied Categorical Structures
    Volume4
    Issue number2-3
    Publication statusPublished - 1996

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    Keywords

    • Enriched category
    • Quantale
    • Quantic sheaf
    • Ring representation

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