What is an exact dg category?
Xiaofa Chen
University of Science and Technology of China, Hefei, P. R. China

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Abstract
Exact dg categories are a simultaneous generalisation of exact categories in the sense of Quillen and of pretriangulated dg categories in the sense of Bonda–Kapranov. The notion is also a differential graded analogue of Barwick's notion of exact -category and a differential graded enhancement of Nakaoka–Palu's notion of extriangulated category. In this paper, we present the definition and a number of fundamental results concerning the dg nerve, the dg derived category, tensor products and functor categories with exact dg target. We conclude with a generalisation of Rump's theorem on the existence of the greatest exact structure on an additive category.