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періодичних видань НАН України
Dg algebras with enough idempotents, their dg modules and their derived categories
Репозиторій DSpace/Manakin
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Dg algebras with enough idempotents, their dg modules and their derived categories
Інший ID:
2010 MSC:Primary 16E45, 18E30; Secondary 16E35, 18E25.
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
483
Завантажень:
235
Анотація:
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.
