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arrow g bijection called cartesian closed category category of sets category theory Chapter cocone codomain coequalizer colimit commutative diagram component composite concept cone constant corresponding countable data type defined definition denote described domain empty epimorphism equalizer equations equivalence relation eval example Exercise fact fibration finite products fixed point follows FP sketch free monoid functor F fuzzy set give given graph homomorphism graph Q Hom(A Hom(C identity arrow implies inclusion induced initial model injective integers inverse left adjoint linear sketch mathematical monic monoid homomorphism monomorphism morphism natural isomorphism natural numbers object natural transformation notation objects and arrows opfibration pair of arrows partial functions poset preserves programming language proj2 proji proof Proposition pullback pushout recursive satisfies Section semantics semigroup Show source and target split structure subcategory subobject subset succ Suppose surjective takes terminal object Theorem tion topos underlying functor unique arrow universal element variable w-CPO