On pushing out frames
Bernhard Banaschewski (1990)
Commentationes Mathematicae Universitatis Carolinae
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Displaying similar documents to “Relatively boolean and De Morgan toposes and locales”
On pushing out frames
On the injectivity of Boolean algebras
Bernhard Banaschewski (1993)
Commentationes Mathematicae Universitatis Carolinae
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The functor taking global elements of Boolean algebras in the topos of sheaves on a complete Boolean algebra is shown to preserve and reflect injectivity as well as completeness. This is then used to derive a result of Bell on the Boolean Ultrafilter Theorem in -valued set theory and to prove that (i) the category of complete Boolean algebras and complete homomorphisms has no non-trivial injectives, and (ii) the category of frames has no absolute retracts.
Weakly monadic Boolean extension functors
J. Dukarm (1980)
Fundamenta Mathematicae
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Spaces with Boolean assemblies
H. Simmons (1980)
Colloquium Mathematicae
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Topological representation for monadic implication algebras
Abad Manuel, Cimadamore Cecilia, Díaz Varela José (2009)
Open Mathematics
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In this paper, every monadic implication algebra is represented as a union of a unique family of monadic filters of a suitable monadic Boolean algebra. Inspired by this representation, we introduce the notion of a monadic implication space, we give a topological representation for monadic implication algebras and we prove a dual equivalence between the category of monadic implication algebras and the category of monadic implication spaces.
Booleanization
B. Banaschewski, A. Pultr (1996)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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