Geodesic
On the injectivity of Boolean algebras
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 501-511

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The functor taking global elements of Boolean algebras in the topos $\text{$\bold{Sh}\frak B$}$ of sheaves on a complete Boolean algebra $\frak B$ 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 $\frak B$-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.
Classification : 03E25, 03E40, 03G05, 06A23, 06E10, 06E99, 18B25, 18B99
Keywords: sheaves on a complete Boolean algebra; injective Boolean algebra; complete Boolean algebra; injective complete Boolean algebra; absolute frame retract 
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     title = {On the injectivity of {Boolean} algebras},
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     zbl = {0789.06007},
     language = {en},
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Banaschewski, B. On the injectivity of Boolean algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 501-511. http://geodesic.mathdoc.fr/item/CMUC_1993__34_3_a11/