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The Weight Criterion, Dong Property, and Manin Products of Operads
We establish that, for a binary operad Var, the Hadamard product of Var and the operad Nov of Novikov algebras is a binary operad (i.e., coincides with their Manin white product Nov $\circ$ Var) if and only if the quadratic part of Var governs a 2-variety. The condition Nov $\circ$ Var $=$ Nov $\oti
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