ScalingStacks

Remark 2.7. For technical reasons, in the cochain analogue of Theorem 2.3 we must also insist that $S$ is simply connected in the sense of Definition 2.6. This is due to the lack of symmetry in the theory of chain and cochain DGAs mentioned in the introduction: one is able to construct a theory for chain DGAs, but in order to construct a viable dual theory for cochain DGAs one has to introduce the assumption of simply connectedness; see, for example, [2].