Dg algebras with enough idempotents, their dg modules and their derived categories
We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that the classical covariant tensor-Hom and contravariant Hom-Hom adjunctions of modules...
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| Datum: | 2017 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Lugansk National Taras Shevchenko University
2017
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/363 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543150580957184 |
|---|---|
| author | Saorín, Manuel |
| author_facet | Saorín, Manuel |
| author_sort | Saorín, Manuel |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-04-10T07:40:45Z |
| description | We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that the classical covariant tensor-Hom and contravariant Hom-Hom adjunctions of modules over associative unital algebras are extended as dg adjunctions between categories of dg bimodules. The corresponding adjunctions of the associated triangulated functors are studied, and we investigate when they are one-sided parts of bifunctors which are triangulated on both variables. We finally show that, for a dg algebra with enough idempotents, the perfect left and right derived categories are dual to each other. |
| first_indexed | 2026-02-08T07:57:54Z |
| format | Article |
| id | admjournalluguniveduua-article-363 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2026-02-08T07:57:54Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-3632017-04-10T07:40:45Z Dg algebras with enough idempotents, their dg modules and their derived categories Saorín, Manuel Dg algebra, dg module, dg category, dg functor, dg adjunction, homotopy category, derived category, derived functor 16E45, 18E30, 16E35, 18E25 We develop the theory dg algebras with enough idempotents and their dg modules and show their equivalence with that of small dg categories and their dg modules. We introduce the concept of dg adjunction and show that the classical covariant tensor-Hom and contravariant Hom-Hom adjunctions of modules over associative unital algebras are extended as dg adjunctions between categories of dg bimodules. The corresponding adjunctions of the associated triangulated functors are studied, and we investigate when they are one-sided parts of bifunctors which are triangulated on both variables. We finally show that, for a dg algebra with enough idempotents, the perfect left and right derived categories are dual to each other. Lugansk National Taras Shevchenko University Ministerio de Economía y Competitividad of Spain, and Fundación "Séneca" of Murcia. 2017-04-10 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/363 Algebra and Discrete Mathematics; Vol 23, No 1 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/363/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/363/153 Copyright (c) 2017 Algebra and Discrete Mathematics |
| spellingShingle | Dg algebra dg module dg category dg functor dg adjunction homotopy category derived category derived functor 16E45 18E30 16E35 18E25 Saorín, Manuel Dg algebras with enough idempotents, their dg modules and their derived categories |
| title | Dg algebras with enough idempotents, their dg modules and their derived categories |
| title_full | Dg algebras with enough idempotents, their dg modules and their derived categories |
| title_fullStr | Dg algebras with enough idempotents, their dg modules and their derived categories |
| title_full_unstemmed | Dg algebras with enough idempotents, their dg modules and their derived categories |
| title_short | Dg algebras with enough idempotents, their dg modules and their derived categories |
| title_sort | dg algebras with enough idempotents, their dg modules and their derived categories |
| topic | Dg algebra dg module dg category dg functor dg adjunction homotopy category derived category derived functor 16E45 18E30 16E35 18E25 |
| topic_facet | Dg algebra dg module dg category dg functor dg adjunction homotopy category derived category derived functor 16E45 18E30 16E35 18E25 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/363 |
| work_keys_str_mv | AT saorinmanuel dgalgebraswithenoughidempotentstheirdgmodulesandtheirderivedcategories |