Topoi, the Categorial Analysis of Logic |
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arrow f assigns axiom bijection Bn(I Boolean bundle C-arrow C-object category theory Chapter characterisation classical co-product codomain collection complement component concept construction corresponding defined definition denoted diagram commute disjoint domain epic equaliser equivalent EXAMPLE EXERCISE exists exponential adjoint extensional finite formula function f functor ƒ and g germs given hence Heyting algebra identity arrow implies inclusion interpretation intuitionistic isomorphic lattice left adjoint Lemma logic M₂ mathematical monic monoid N-Set natural numbers object natural transformation notion open sets output pair partial elements poset pr₁ pre-order precisely PROOF pseudo-complement pullback recursion relation satisfies semantics sentence set theory sheaf sheaves Show singleton square stalk structure Sub(d subobject classifier subset terminal object Theorem Top(I topoi topological space topology topos transitive true truth truth-values unique arrow v₁ valid well-pointed ΩΧΩ