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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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2017 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155937 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716965068472320 |
|---|---|
| author | Saorín, M. |
| author_facet | Saorín, M. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-12-07T18:08:03Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155937 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:08:03Z |
| publishDate | 2017 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Saorín, M. 2019-06-17T15:36:49Z 2019-06-17T15:36:49Z 2017 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. https://nasplib.isofts.kiev.ua/handle/123456789/155937 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. The author is highly indebted to Alexander Zimmermann for the careful reading of these notes, for his comments and for his help in improving the presentation. This work is backed by reseach projects from the Ministerio de Economía y Competitividad of Spain(MTM201346837-P and MTM201677445-P) and the Fundación ’Séneca’ of Murcia(19880/GERM/15), both with a part of FEDER funds. We thank these institutions for their support. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Dg algebras with enough idempotents, their dg modules and their derived categories Article published earlier |
| spellingShingle | Dg algebras with enough idempotents, their dg modules and their derived categories Saorín, M. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155937 |
| work_keys_str_mv | AT saorinm dgalgebraswithenoughidempotentstheirdgmodulesandtheirderivedcategories |