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Anti-successors and anti-replicators, Manin products and Koszul duality
We develop an operadic theory of anti-splitting and anti-replication for binary operads. For a binary operad $\opd$, we define its anti-bisuccessor $\ABSu(\opd)$ and anti-trisuccessor $\ATSu(\opd)$, with the property that an operation of $\opd$ splits into a negative sum of two or three operations,
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