Multiplication objects (Q2738453)
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scientific article; zbMATH DE number 1639629
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Multiplication objects |
scientific article; zbMATH DE number 1639629 |
Statements
3 April 2002
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monoidal categories
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Abelian categories
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Grothendieck categories
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multiplication objects
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comodules
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Doi-Koppinen modules
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graded rings
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braided monoidal categories
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multiplication modules
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cocommutative coalgebras
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Multiplication objects (English)
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A concept of a multiplication object in a monoidal category is introduced, generalizing multiplication modules, multiplication modules relative to a torsion theory, and multiplication graded modules. Some interesting particular cases are investigated, such as multiplication objects in the category of right comodules over a cocommutative coalgebra, and multiplication objects in a category of Doi-Koppinen modules. It is proved that the endomorphism ring of an indecomposable multiplication object is local in any Abelian braided monoidal category.NEWLINENEWLINEFor the entire collection see [Zbl 0963.00025].
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