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Edit : There are several satisfying proofs in the case each $L^i$ is finite-dimensional. It is proven (for example, Hinich DG coalgebras as formal stacks) that for $A$ : local Artin ring then $\...

Let $\mathfrak g:=(V,d,[\cdot,\cdot])$ be a differential graded Lie algebra (DGLA) where $d$ is the zero differential. Intrinsic formality: The DGLA $\mathfrak g$ will be said intrinsically formal ...