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adjoint functors asserts assume C-monoid calculation called canonical subobjects cartesian closed category category theory characteristic morphism closed term completes the proof computable construction Corollary deductive system defined Definition diagram element epimorphism equations Example Exercise finite free topos free variables Freyd functional completeness functor categories given graph hence Heyting algebra holds indeterminate arrow induction initial object internal language intuitionistic type theory isomorphism kernel Lambek Lawvere left adjoint Lemma logicians mapping monoid monomorphism Moreover morphism natural numbers object natural transformation numerical functions obtain polynomial preordered set preserves prime filter primitive recursive functions proof of Proposition Proposition 6.1 provable prove pullback pure type theory reader representable rule of choice rules of inference Section sheaf strict logical functor subset Suppose surjective term forming operations term of type terminal object Top0 topos toposes triple typed A-calculus unique arrow universal property variable of type weak natural numbers write
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JEAN-YVES GIRARD, PAUL TAYLOR, YVES LAFONT
JOSEPH A GOGUEN, ROD M BURSTALL
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Introduction to higher order categorical logic
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