  Generalized complex geometry was classically formulated by the language of
differential geometry. In this paper, we reformulated a generalized complex
manifold as a holomorphic symplectic differentiable formal stack in a
homotopical sense. Meanwhile, by developing the machinery for shifted
symplectic formal stack, we prove that the coisotropic intersection inherits
shifted Poisson structure. Generalized complex branes are also studied.
