Differential Graded Categories are k-linear Stable Infinity Categories

TL;DR

This paper establishes an equivalence between pretriangulated differential graded categories and k-linear stable infinity categories, providing a bridge between algebraic and higher categorical frameworks.

Contribution

It demonstrates that the infinity category of pretriangulated differential graded categories over a field of characteristic zero is equivalent to the infinity category of k-linear stable infinity categories.

Findings

Model category structure on differential graded categories over k

Equivalence between the underlying infinity category and k-linear stable infinity categories

Identification of fibrant objects as pretriangulated differential graded categories

Abstract

We describe a comparison between pretriangulated differential graded categories and certain stable infinity categories. Specifically, we use a model category structure on differential graded categories over k (a field of characteristic 0) where the weak equivalences are the Morita equivalences, and where the fibrant objects are in particular pretriangulated differential graded categories. We show the underlying infinity category of this model category is equivalent to the infinity category of k-linear stable infinity categories.