Topoi, the Categorial Analysis of Logic

6-arrow 8-object A₁ arrow f assigns axioms bijection Bn(I Boolean bundle category theory characterisation classical co-product codomain collection component concept construction corresponding defined definition denoted diagram commute domain epic equaliser equivalent EXAMPLE EXERCISE exists extensional f and g F₁ finite formula function f functor germs given hence Heyting algebra identity arrow implies inclusion interpretation intuitionistic isomorphic lattice left adjoint Lemma logic 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 X₁ Ω Ω ΩΧΩ