## Coherence in Categories |

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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 corresponding covariant cut-elimination cut-elimination theorem define definition diagram of type diagrams commute discrete club dist(P elements equivalent expanded instances extra structure following diagram free model free object full subcategory functor category G.M. Kelly given graph hence 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 numbers natural transformations notation objects paper path permutation polycategory pre-category pre-clubs prime factors proof proper Proposition rank rappel reduced to proving relation right adjoint satisfies sequence shapes Supp Suppose symmetric monoidal categories Szabo tensor product theory tion transformation f type A morphisms unblocked string unique variables write