A theory of quantal sets
type: Item
instance of: scholarly article
title: A theory of quantal sets
zbMATH Open document ID: 0685.18006
DOI: 10.1016/0022-4049(89)90147-3
author: Ugo Berni-Canani
author: Rosanna Succi-Cruciani
author: F. Borceux
published in: Journal of Pure and Applied Algebra
publication date: 1989-01-01T00:00:00Z
review text: The authors introduce a more elaborate analogue for quantales [\textit{F. Borceux} and \textit{G. van den Bossche}, Order 3, 61-87 (1986; Zbl 0595.18003)] of sheaves of a locale. A Q-set for a quantale Q is defined as a set A with a Q-valued relation \(''='': A\times A\to Q\) which is transitive \((a=a'\&a'=a''\leq a=a'')\) and satisfies a weakened version of symmetry. Q-sets lead to a fibration \(\underset \tilde{} {E} Q\) whose fibers are toposes. The properties of this construction are developed with the aim of showing that it gives an adequate version of sheaves.
Mathematics Subject Classification ID: 18F20
Mathematics Subject Classification ID: 06B23
Mathematics Subject Classification ID: 18B25
Mathematics Subject Classification ID: 03E40
zbMATH DE Number: 4122192
zbMATH Keywords: quantale-valued set
zbMATH Keywords: sheaves of a locale
zbMATH Keywords: fibration
reviewed by: J. R. Isbell
MaRDI profile type: Publication
full work available at URL: 0022-4049(89)90147-3
OpenAlex ID: W2058418039
cites work: Quantales and their sheaves
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cites work: Sheaves on sites as Cauchy-complete categories
description: scientific article; zbMATH DE number 4122192