Morita duality emerging from quasi-abelian categories
Autor: | Wolfgang Rump |
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Rok vydání: | 2021 |
Předmět: | |
Zdroj: | Algebras and Representation Theory. 25:1309-1322 |
ISSN: | 1572-9079 1386-923X |
Popis: | 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. |
Databáze: | OpenAIRE |
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