Charles University in Prague, Faculty of Mathematics and Physics
Abstract
summary:The functor taking global elements of Boolean algebras in the topos \text{\bold{Sh}\frak 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