Mittag-Leffler inverse systems of DG categories

We will introduce a certain class of sufficiently nice inverse systems of DG categories, which we call (secondary) Mittag-Leffler systems. The basic examples are given by the formal schemes and their noncommutative generalization. It can be shown that for ML systems a certain non-standard inverse limit (in the dualizable world) has a reasonable description, and it generalizes the category of nuclear modules. Moreover, we expect that for ML systems the K-theory commutes with inverse limits.