  We show that the functor from curved differential graded algebras to
differential graded categories, defined by the second author in [B], sends
Cartesian diagrams to homotopy Cartesian diagrams, under certain reasonable
hypotheses. This is an extension to the arena of dg categories of a
construction of projective modules due to Milnor. As an example, we show that
the functor satisfies descent for certain partitions of a complex manifold.
