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Lattices of homomorphisms

Part of: Special properties Boolean algebras (Boolean rings) Distributive lattices Categories with structure Algebraic logic

Published online by Cambridge University Press:  09 April 2009

B. A. Davey  and
H. A. Priestley
B. A. Davey
Affiliation:
Department of Pure Mathematics, La Trobe University, Bundoora, Victoria 3083, Australia
H. A. Priestley
Affiliation:
Mathematical Institute, 24/29 St. Giles, Oxford OX1 3LB, England
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Abstract

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Given a variety K of lattice-ordered algebras, A ∈ K is catalytic if for all B ∈ K, K(A, B) is a lattice for the pointwise order. The catalytic objects are determined for various varieties of distributive-lattice-ordered algebras. The characterisations obtained do not show an overall unity and exhibit diverse behaviour. Duality is employed extensively. Its usefulness in this context depends on the existence of an order-isomorphism between K(A, B) and the corresponding dual horn-set. Criteria for the existence of such an order-isomorphism are investigated for dualities of the Davey-Werner type. The relationship between catalytic objects and colattices is also discussed.

MSC classification

Secondary: 03G10: Lattices and related structures 06D15: Pseudocomplemented lattices 18D35: Structured objects in a category (group objects, etc.) 54F05: Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 40 , Issue 3 , June 1986 , pp. 364 - 406
Copyright
Copyright © Australian Mathematical Society 1986

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