Abstract
The main result then has to be rephrased as a necessary and sufficient condition for an obstruction theory to be induced by a derived structure. If a compatible system of liftings of the obstruction theory to inductively defined square-zero extensions exists, then it is induced by a derived structure. Conversely, if the obstruction theory is induced by a derived structure, such an inductive system exists by using the Postnikov decomposition. The precise statement is the following:
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