On the injectivity of Boolean algebras
Banaschewski, Bernhard
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993), p. 501-511 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 1993-01-01
Classification:  03E25,  03E40,  03G05,  06A23,  06E10,  06E99,  18B25,  18B99 
@article{118606,
     author = {Bernhard Banaschewski},
     title = {On the injectivity of Boolean algebras},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {34},
     year = {1993},
     pages = {501-511},
     zbl = {0789.06007},
     mrnumber = {1243081},
     language = {en},
     url = {http://dml.mathdoc.fr/item/118606}
}

Banaschewski, Bernhard. On the injectivity of Boolean algebras. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) pp. 501-511. http://gdmltest.u-ga.fr/item/118606/

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