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CATEGORIES OF BOOLEAN SHEAVES OF ALGEBRAS
CATEGORIES OF BOOLEAN SHEAVES OF SIMPLE ALGEBRAS
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algebraic theory amalgamated sum Baer rings Boolean algebra Boolean spaces canonical category ft coequaliser cokernel commutative rings comonad complemented counion couniversal defined denote direct factors direct image element equivalence of categories equivalence relations factorises fibred product filtered colimits filtered union finite rank finite type finitely generated regular finitely presentable category finitely presentable objects follows forgetful functor full subcategory homomorphism IBool idempotent initial object isomorphism k-algebras kernel left adjoint left closed Let us show locally Boolean sheaves locally finitely presentable locally indecomposable categories locally Noetherian locally simple categories locally simple subcategory morphism f morphism of locally non-unitary normal monomorphism normal subobjects null object objects of finite objects of ft pa9es phism preserves filtered colimits preserves finite products Proceedin9s profinite group Proof Proposition regular epimorphism regular quotient objects resp satisfying semi-epimorphism sheaves of simple simple objects Spec strongly lattice-ordered structural sheaf subcategory of ft Theorem