Morita duality emerging from quasi-abelian categories

Autor:	Wolfgang Rump
Rok vydání:	2021
Předmět:	Pure mathematics Property (philosophy) Mathematics::Operator Algebras General Mathematics Duality (mathematics) Dual (category theory) Mathematics::K-Theory and Homology Mathematics::Category Theory Morita therapy Embedding Locally compact space Abelian group Vector space Mathematics
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
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::040ce06724a56434596fbb3cfc3b8f4e https://doi.org/10.1007/s10468-021-10068-4 Zobrazit plný text záznamu Full text from SpringerLink