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When is $C\text-\mathsf{dg\text-mod}$ determined by the connective base changes?
I'm using cohomological gradings.
For $C\in k\text-\mathsf{cdga}$ (where $k$ can be taken of characteristic 0), a morphism $C\to A$ to a connective dg-algebra $A\in k\text-\mathsf{cdga}_{\leq0}$ ...
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