An informal introduction to dg categories

TL;DR

This paper provides an informal overview of differential graded (dg) categories, emphasizing their foundational role compared to triangulated categories and discussing the dg quotient construction by Keller and Drinfeld.

Contribution

It offers an accessible introduction to dg categories, highlighting their basic properties and the dg quotient concept, which is less developed than triangulated categories.

Findings

Dg categories are more fundamental than triangulated categories.

The paper reviews the dg quotient construction by Keller and Drinfeld.

Provides foundational insights into dg categories for further research.

Abstract

In this informal introduction to dg categories, the slogan is that dg categories are more rudimentary than triangulated categories. We recall some details on the dg quotient category introduced by Bernhard Keller and Vladimir Drinfeld.