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2-functor Adec algebra arrows assertion associative augmentation axioms cartesian closed categories Cat/E central morphism closed categories closed functor closed loops codomain coherence problem coherence result coherence theorem commutative diagram compatible components composite congruence constant constructible corresponding covariant cut-elimination cut-elimination theorem define definition diagram of type diagrams commute discrete club dist(P domain Edited elements equivalent expanded instances extra structure finite following diagram free model full subcategory functor category G-sets G.M. Kelly given graph identity incompatible induction instantiation inverses K-algebra K-categories Lambek Lemma Mac Lane Mdec monoidal functor N-allowable N-central N-constructible N-graph N-shapes natural isomorphisms natural transformations notation objects paper path permutation polycategory pre-clubs prime factors proof Proposition rank rappel reduced to proving relation right adjoint satisfies Seiten Seminaire sequence shapes Supp Suppose symmetric monoidal categories Szabo tensor product Theory tion transformation f unique variables write