A nonmonoidal closed category is a category with an internal homomorphism functor, left Yoneda natural arrows, unity object and some natural transformations and coherence axioms.The object of this paper is to give a complete solution of the coherence problem in this structure: we use a cut-elimination theorem as basic tool to prove that the elementary natural transformations are characterized by their graph (roughly speaking the graph is the type of identification imposed by a natural transformation on the arguments of its domain and codomain).
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Miguel L. Laplaza (1977) studied this question.
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