Relatively boolean and De Morgan toposes and locales

Anders Kock; Gonzalo E. Reyes

Displaying similar documents to “Relatively boolean and De Morgan toposes and locales”

On pushing out frames

Bernhard Banaschewski (1990)

Commentationes Mathematicae Universitatis Carolinae

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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 $𝐒𝐡 𝔅$ of sheaves on a complete Boolean algebra $𝔅$ 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 $𝔅$ -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.