Arrows, Structures, and Functors: The Categorical Imperative |
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A(FB A₁ a₂ abelian monoid Abm-structure admissible algebra arbitrary arrows axioms bijection category of sets category theory co-optimal coequalizer cofree colimit commutes composition construction coproduct defined DEFINITION diagram Dyn(X dynamorphism E)-algebras element epimorphism eq(f equalizers equivalence relation example exercise exists a unique F₁ finite forgetful functor function f Hint identity image factorization system inverse isomorphism K₁ K₂ left adjoint Let f linear maps Lipschitz maps map ƒ Met1 metric spaces minimal realization monad monoid homomorphism monoidal category monomorphism morphism natural transformation object one-element one-to-one optimal order-preserving p₁ pair phism poset preserves products Proof PROPOSITION Prove q in Q q₁ QXXo reachability reader respect to G right adjoint satisfies Section sequential machines sets with structure Show solution set subset subspace T-algebra THEOREM topology V-category Vect vector space Verify Πι