The functor category of a finitely accessible additive category (Q2904599)
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scientific article; zbMATH DE number 6065792
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The functor category of a finitely accessible additive category |
scientific article; zbMATH DE number 6065792 |
Statements
14 August 2012
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accessible categories
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Grothendieck categories
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limit
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pure injective object
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The functor category of a finitely accessible additive category (English)
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In this paper the authors prove some important properties for finitely accessible additive categories. If \(\mathcal{A}\) is a finitely accessible additive category then: (i) any object has a pure-injective envelope (Theorem 1); (ii) \(\mathcal{A}\) is quasi-complete (Corollary 2); (iii) the set \(\mathrm{Ind}(\mathcal{A})\) of the indecomposable pure-injective objects in \(\mathcal{A}\), up to isomorphism, is a pure cogenerator for \(\mathcal{A}\) (Corollary 6).
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