A derived affine scheme is a special kind of generalized scheme.
In a version of the theory of derived algebraic stack?s due to Toën, Vezzosi and Vaquie, the category of derived affine schemes is , the opposite of the category of simplicial commutative unital rings. The category of simplicial presheaves on has several model category structures. If a projective model structure is used, this category of simplicial presheaves is denoted where weak equivalences and fibrations are defined levelwise. By one denotes the left Bousfield localization of the model category with respect to the Yoneda images of equivalences in ; this model category is called the model category of prestacks over . The fibrant objects in are the simplicial presheaves such that
(anodyne condition) for all , the simplicial set is fibrant; and
(prestack condition) for each equivalence in , the induced morphism is a weak equivalence of simplicial sets.