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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Embedding of closed categories into monoidal closed categories


Author: Miguel L. Laplaza
Journal: Trans. Amer. Math. Soc. 233 (1977), 85-91
MSC: Primary 18D15
DOI: https://doi.org/10.1090/S0002-9947-1977-0480686-8
MathSciNet review: 0480686
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Abstract: S. Eilenberg and G. M. Kelly have defined a closed category as a category with internal homomorphism functor, left Yoneda natural arrows, unity object and suitable coherence axioms. A monoidal closed category is a closed category with an associative tensor product which is adjoint to the int-hom. This paper proves that a closed category can be embedded in a monoidal closed category: the embedding preserves any associative tensor product which may exist. Besides the usual tools of the theory of closed categories the proof uses the results of B. Day on promonoidal structures.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1977-0480686-8
Keywords: Closed category, monoidal category, monoidal closed category, monoidal biclosed category, internal homomorphism functor, tensor product, promonoidal structure
Article copyright: © Copyright 1977 American Mathematical Society