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Dg algebras with enough idempotents, their dg modules and their derived categories

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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Main Author: Saorín, M.
Format: Article
Language:English
Published: Інститут прикладної математики і механіки НАН України 2017
Series:Algebra and Discrete Mathematics
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/155937
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spelling 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 2023-05-20T17:48:24Z
last_indexed 2023-05-20T17:48:24Z
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