On Drinfeld's DG quotient

The possibility of constructing quotients of differential graded (=dg) categories is essential in non-commutative algebraic geometry. The first construction of dg quotients appeared in Keller's work (Keller (1994) [21]) and it was recently followed by Drinfeld's elegant approach (Drinfeld (2004) [9]). Although Drinfeld's dg quotient admits a very simple construction, it didn't seem to be intrinsically defined. In this article we complete this aspect of Drinfeld's work by providing three different characterizations of Drinfeld's dg quotient in terms of simple universal properties.