On the injectivity of Boolean algebras
نویسنده
چکیده
The functor taking global elements of Boolean algebras in the topos ShB 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.
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