Quasi DG categories and mixed motivic sheaves

TL;DR

This paper introduces quasi DG categories, generalizes DG categories, and constructs a triangulated category of mixed motives over a base variety using these concepts.

Contribution

It defines quasi DG categories, extends the notion of DG categories, and constructs a triangulated category of mixed motives via $C$-diagrams.

Findings

Homotopy category of $C$-diagrams forms a triangulated category

Provides a new framework for mixed motives over a base variety

Generalizes DG categories to quasi DG categories

Abstract

We introduce the notion of a quasi DG category, generalizing that of a DG category. To a quasi DG category satisfying certain additional conditions, we associate another quasi DG category, the quasi DG category of $C$-diagrams. We then show the homotopy category of the quasi DG category of $C$-diagrams has the structure of a triangulated category. This procedure is then applied to produce a triangulated category of mixed motives over a base variety.