2020/02/04 by Miyachi, Jun-ichi, Nagase}, Hiroshi
#Category Theory (math.CT) #FOS: Mathematics
paper · doi:10.48550/arxiv.2002.01130
We study N-differential graded (NDG) categories and their the derived categories. First, we introduce N-differential modules over an NDG category A. Then we show that the category CNdg(A) of N-differential A-modules is a Frobenius category, and that its homotopy category KNdg(a) is a triangulated category. Second, we study the properties of the derived category DNdg(A) and give triangle equivalences of Morita type between derived categories of NDG categories. Finally, we show DNdg(A) is triangle equivalent to the derived category of some ordinary DG category.