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Necessity of shapes for coherence results in category theory
The classic coherence theorems of MacLane (Natural associativity and commutativity, Rice U. studies, 1963) talked about natural transformations between functors. … By 1971 (Kelly-MacLane, Coherence in closed categories, JPAA) and 1972 (Kelly, An abstract approach to coherence, LNM 281), functors had been replaced by "shapes"---formal combinations of given functors …