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: | English |
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Інститут прикладної математики і механіки НАН України
2017
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| Schriftenreihe: | Algebra and Discrete Mathematics |
| Online Zugang: | http://dspace.nbuv.gov.ua/handle/123456789/155937 |
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| Zitieren: | Dg algebras with enough idempotents, their dg modules and their derived categories / M. Saorín // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 62-137. — Бібліогр.: 25 назв. — англ. |
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irk-123456789-1559372019-06-18T01:27:48Z Dg algebras with enough idempotents, their dg modules and their derived categories Saorín, M. 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. 2017 Article Dg algebras with enough idempotents, their dg modules and their derived categories / M. Saorín // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 62-137. — Бібліогр.: 25 назв. — англ. 1726-3255 2010 MSC:Primary 16E45, 18E30; Secondary 16E35, 18E25. http://dspace.nbuv.gov.ua/handle/123456789/155937 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Saorín, M. |
| spellingShingle |
Saorín, M. Dg algebras with enough idempotents, their dg modules and their derived categories Algebra and Discrete Mathematics |
| author_facet |
Saorín, M. |
| author_sort |
Saorín, M. |
| title |
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_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_sort |
dg algebras with enough idempotents, their dg modules and their derived categories |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2017 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155937 |
| citation_txt |
Dg algebras with enough idempotents, their dg modules and their derived categories / M. Saorín // Algebra and Discrete Mathematics. — 2017. — Vol. 23, № 1. — С. 62-137. — Бібліогр.: 25 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT saorinm dgalgebraswithenoughidempotentstheirdgmodulesandtheirderivedcategories |
| first_indexed |
2025-07-14T08:08:39Z |
| last_indexed |
2025-07-14T08:08:39Z |
| _version_ |
1837609013503590400 |