We show that the functor from curved differential graded algebras to differential graded categories, defined by the second author, 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.
Bibliographical noteFunding Information:
The first author acknowledges the support of the European Commission under the Marie Curie Programme for the IEF grant which enabled this research to take place. The contents of this article reflect the views of the two authors and not the views of the European Commission.
J.B. partially supported by NSF grant DMS10-07113.
- dg categories
- projective modules
ASJC Scopus subject areas
- Algebra and Number Theory
- Geometry and Topology