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Morita duality emerging from quasi-abelian categories

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Abstract

It is shown that a general concept of Morita duality between abelian categories with no generating hypothesis for reflexive objects is completely described by a special class of quasi-abelian categories, called ample Morita categories. The duality takes place between a pair of intrinsic abelian full subcategories which exist for any quasi-abelian category. Morita categories, being slightly more general, admit a natural embedding into ample ones. An existence criterion for a duality of a Morita category is proved. It generalizes Pontrjagin duality for the category of locally compact abelian groups which is shown to be a non-ample non-classical Morita category. More examples of non-classical Morita categories are obtained from dual systems of topological vector spaces satisfying the Hahn-Banach property.

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Acknowledgements

The author is grateful to an anonymous referee for spotting typos and suggesting a better terminology with respect to Colby-Fuller duality and its covariant generalization in this paper.

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  1. Institute for Algebra und Number Theory, University of Stuttgart, Pfaffenwaldring 57, D-70550, Stuttgart, Germany

    Wolfgang Rump

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  1. Wolfgang Rump
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Rump, W. Morita duality emerging from quasi-abelian categories. Algebr Represent Theor 25, 1309–1322 (2022). https://doi.org/10.1007/s10468-021-10068-4

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