Topoi: The Categorial Analysis of Logic

adjoint algebra arrow assigns axiom Boolean C-arrow called Chapter character classical classifier closed collection commutes complete component composite concept condition consider constant construction continuous corresponding defined definition denoted described determined developed diagram domain elements epic equality equivalent EXAMPLE EXERCISE exists exponential expression extensional fact follows formula function functor given gives hence holds identified identity implies inclusion interpretation intuitionistic logic isomorphic language logic mathematical means monic notion object obtain operations pair partial particular poset precisely principle PROOF Prove pullback relation result rules satisfies sentence set theory sheaf sheaves Show space square statement structure subobject subset Suppose symbol Theorem topoi topology topos transitive true truth truth-values unique universal valid variables yields