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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Morita contexts of enriched categories

Authors: J. Fisher-Palmquist and P. H. Palmquist
Journal: Proc. Amer. Math. Soc. 50 (1975), 55-60
MSC: Primary 18D20
MathSciNet review: 0419559
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Abstract: Categories enriched over a closed category $ {\mathbf{V}}$ are considered. The theorems and proofs are nonadditive while specializing when $ {\mathbf{V}}$ is the category of abelian groups to yield different interpretations and proofs of old results. $ {\mathbf{V}}$-adjoint equivalences of certain $ {\mathbf{V}}$-functor categories are shown to correspond to generalized Morita equivalences between small $ {\mathbf{V}}$-categories. Morita contexts are given a simple description as certain cospans and are shown to support a $ 2$-dimensional structure.

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Keywords: Closed category, enriched category, functor category, adjoint equivalence, Kan extension, cospan, dense, bicategory, $ 2$-dimensional category, Morita context, Morita equivalence, atom
Article copyright: © Copyright 1975 American Mathematical Society

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