Functor category dualities for varieties of Heyting algebras
نویسندگان
چکیده
Let A be a 4nitely generated variety of Heyting algebras and let SI(A) be the class of subdirectly irreducible algebras in A. We prove that A is dually equivalent to a category of functors from SI(A) into the category of Boolean spaces. The main tool is the theory of multisorted natural dualities. c © 2002 Elsevier Science B.V. All rights reserved. MSC: Primary: 06D20; 06D50; secondary: 08C05; 08A35
منابع مشابه
Optimal natural dualities for varieties of Heyting algebras
The techniques of natural duality theory are applied to certain finitely generated varieties of Heyting algebras to obtain optimal dualities for these varieties, and thereby to address algebraic questions about them. In particular, a complete characterisation is given of the endodualisable finite subdirectly irreducible Heyting algebras. The procedures involved rely heavily on Priestley duality...
متن کاملMartin Frontal operators in weak Heyting algebras
In this paper we shall introduce the variety FWHA of frontal weak Heyting algebras as a generalization of the frontal Heyting algebras introduced by Leo Esakia in [10]. A frontal operator in a weak Heyting algebra A is an expansive operator τ preserving finite meets which also satisfies the equation τ(a) ≤ b ∨ (b → a), for all a, b ∈ A. These operators were studied from an algebraic, logical an...
متن کاملOn generalizing free algebras for a functor
In this paper we introduce a new setting, based on partial algebras, for studying constructions of finitely generated free algebras. We give sufficient conditions under which the finitely generated free algebras for a variety V may be described as the colimit of a chain of finite partial algebras obtained by repeated application of a functor. In particular, our method encompasses the constructi...
متن کاملInitial Normal Covers in Bi-heyting Toposes
The dual of the category of pointed objects of a topos is semiabelian, thus is provided with a notion of semi-direct product and a corresponding notion of action. In this paper, we study various conditions for representability of these actions. First, we show this to be equivalent to the existence of initial normal covers in the category of pointed objects of the topos. For Grothendieck toposes...
متن کاملDualities for Equational Classes of Brouwerian Algebras and Heyting Algebras
This paper focuses on the equational class S„ of Brouwerian algebras and the equational class L„ of Heyting algebras generated by an »-element chain. Firstly, duality theories are developed for these classes. Next, the projectives in the dual categories are determined, and then, by applying the dualities, the injectives and absolute subretracts in Sn and L„ are characterized. Finally, free prod...
متن کامل