Keller, On differential graded categories

http://jp.arxiv.org/abs/math.KT/0601185

For a long time, triangulated categories were considered too poor to allow the development more than a rudimentary theory. This vision has changed in recent years, but the fact remains that many important constructions in derived categories cannot be performed with triangulated categories. Notably, tensor products and functor categories formed from triangulated categories are no longer triangulated. One approach to overcome these problems has been the theory of derivator initiated by Heller and Grothendieck at the beginning of the nineties. Another, prehaps less formidable one is the theory of differential graded categories (=dg-categoris), together with its cousin, the theory of A_∞categories.

Orlov の定理を Schwartz の核定理の類似と思うと，位相的テンソル積・核型空間の理論に相当するのは何か？