Coherence in nonmonoidal closed categories

Laplaza, Miguel L.

doi:10.1090/S0002-9947-1977-0444740-9

Coherence in nonmonoidal closed categories
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by Miguel L. Laplaza PDF

Trans. Amer. Math. Soc. 230 (1977), 293-311 Request permission

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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