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

• Date: 2017
• Main Author: Saorín, Manuel
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2017
• Subjects: Dg algebra; dg module; dg category; dg functor; dg adjunction; homotopy category; derived category; derived functor; 16E45; 18E30; 16E35; 18E25
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/363
• Journal Title: Algebra and Discrete Mathematics

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...