Abstract
By inspiring ourselves in Drinfeld's DG quotient, we develop Postnikov towers, k-invariants and an obstruction theory for dg categories. As an application, we obtain the following ‘rigidification’ theorem: let A be a homologically connective dg category and F 0 : B → H 0 ( A ) a dg functor to its homotopy category. If the inductive family { ω n ( F n ) } n ⩾ 0 of obstruction classes vanishes, then a lift F : B → A for F 0 exists.
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