Obstruction Theory for Bigraded Differential Algebras

We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted coefficients, as well as a proof of uniqueness. These results are further employed to study automorphism groups of minimal cbba's and to characterize formality in terms of grading automorphisms.