Piggyback dualities revisited

In natural duality theory, the piggybacking technique is a valuable tool for constructing dualities. As originally devised by Davey and Werner, and extended by Davey and Priestley, it can be applied to finitely generated quasivarieties of algebras having term-reducts in a quasivariety for which a we...

Full description

Saved in:
Bibliographic Details
Published inAlgebra universalis Vol. 76; no. 2; pp. 245 - 285
Main Authors Davey, B. A., Haviar, M., Priestley, H. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2016
Springer Nature B.V
Subjects
Algebra
Lattices (mathematics)
Mathematics
Mathematics and Statistics
Theorems
Ockham algebra
06A12
Primary: 08C20
Secondary: 06D50
distributive lattice
natural duality
semilattice
piggyback duality
Online AccessGet full text

Cover

More Information
Summary:In natural duality theory, the piggybacking technique is a valuable tool for constructing dualities. As originally devised by Davey and Werner, and extended by Davey and Priestley, it can be applied to finitely generated quasivarieties of algebras having term-reducts in a quasivariety for which a well-behaved natural duality is already available. This paper presents a comprehensive study of the method in a much wider setting: piggyback duality theorems are obtained for suitable prevarieties of structures. For the first time, and within this extended framework, piggybacking is used to derive theorems giving criteria for establishing strong dualities and two-forone dualities. The general theorems specialise in particular to the familiar situation in which we piggyback on Priestley duality for distributive lattices or Hofmann–Mislove– Stralka duality for semilattices, and many well-known dualities are thereby subsumed. A selection of new dualities is also presented.
ISSN:0002-5240
1420-8911
DOI:10.1007/s00012-016-0395-y