perfect dg-module

Let $T$ be a dg-category and $D(T)$ its derived dg-category. Consider the dg-Yoneda embedding

$h : T \hookrightarrow D(T).$

The thick triangulated subcategory generated by its essential image is denoted $Perf(T) \subset D(T)$. It coincides with the full subcategory of compact objects of $D(T)$.

A dg-module $M \in D(T)$ is **perfect** if it is in the full sub-dg-category generated by the pretriangulated envelope $tri(A)$ under direct summands.

We will write $perf(T) \subset D(T)$ for the full sub-dg-category of $D(T)$ spanned by perfect dg-modules. This is a pretriangulated sub-dg-category.

Section 2.3 of

- Dmitri Orlov,
*Smooth and proper noncommutative schemes and gluing of DG categories*, arXiv:1402.7364.

Paragraph 3.5 of

- Bernhard Keller,
*On differential graded categories*, arXiv:math/0601185.

Last revised on December 15, 2018 at 08:44:51. See the history of this page for a list of all contributions to it.