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Coherence in nonmonoidal closed categories


Author: Miguel L. Laplaza
Journal: Trans. Amer. Math. Soc. 230 (1977), 293-311
MSC: Primary 18D20
DOI: https://doi.org/10.1090/S0002-9947-1977-0444740-9
MathSciNet review: 0444740
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Abstract: A Trionmonoidal 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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0444740-9
Keywords: Closed category, coherence, cut-elimination theorem, graph
Article copyright: © Copyright 1977 American Mathematical Society

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