We introduce the notion of a quasi DG category, and give a procedure to construct a triangulated category associated to it. Then we apply it to the construction of the triangulated category of mixed motivic sheaves over a base variety.
"Relative algebraic correspondences and mixed motivic sheaves." Proc. Japan Acad. Ser. A Math. Sci. 88 (8) 121 - 126, October 2012. https://doi.org/10.3792/pjaa.88.121