### 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 language | English |
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Pages (from-to) | 283-296 |

Number of pages | 14 |

Journal | Applied Categorical Structures |

Volume | 4 |

Issue number | 2-3 |

Publication status | Published - 1996 |

### Keywords

- Enriched category
- Quantale
- Quantic sheaf
- Ring representation

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## Cite this

Ambler, S., & Verity, D. (1996). Generalized logic and the representation of rings.

*Applied Categorical Structures*,*4*(2-3), 283-296.