### 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.

Language | English |
---|---|

Pages | 283-296 |

Number of pages | 14 |

Journal | Applied Categorical Structures |

Volume | 4 |

Issue number | 2-3 |

Publication status | Published - 1996 |

### Fingerprint

### Keywords

- Enriched category
- Quantale
- Quantic sheaf
- Ring representation

### Cite this

*Applied Categorical Structures*,

*4*(2-3), 283-296.

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*Applied Categorical Structures*, vol. 4, no. 2-3, pp. 283-296.

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

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Generalized logic and the representation of rings

AU - Ambler, Simon

AU - Verity, Dominic

PY - 1996

Y1 - 1996

N2 - 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.

AB - 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.

KW - Enriched category

KW - Quantale

KW - Quantic sheaf

KW - Ring representation

UR - http://www.scopus.com/inward/record.url?scp=25144509590&partnerID=8YFLogxK

M3 - Article

VL - 4

SP - 283

EP - 296

JO - Applied Categorical Structures

T2 - Applied Categorical Structures

JF - Applied Categorical Structures

SN - 0927-2852

IS - 2-3

ER -