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Since curved dg algebras, and modules over them, have differentials whosesquare is not zero, these objects have no cohomology, and there is no classicalderived category. For different purposes, different notions of "derived"categories have been introduced in the literature. In this note, we show thatfor some concrete curved dg algebras, these derived categories vanish. Thishappens for example for the initial curved dg algebra whose module category isthe category of precomplexes, and for certain deformations of dg algebras.

On the (non)vanishing of some "derived" categories of curved dg algebras