Proposition 45.9.12. Let $k$ be a field. Let $F$ be a field of characteristic $0$. There is a $1$-to-$1$ correspondence between the following

data (D0), (D1), (D2), and (D3) satisfying (A), (B), and(C), and

$\mathbf{Q}$-linear symmetric monoidal functors

\[ G : M_ k \longrightarrow \text{graded }F\text{-vector spaces} \]such that $G(\mathbf{1}(1))$ is nonzero only in degree $-2$.

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