Abstract
We relate the brace construction introduced by Calaque and Willwacher to an additivity functor. That is, we construct a functor from brace algebras associated to an operad${\mathcal{O}}$to associative algebras in the category of homotopy${\mathcal{O}}$-algebras. As an example, we identify the category of$\mathbb{P}_{n+1}$-algebras with the category of associative algebras in$\mathbb{P}_{n}$-algebras. We also show that under this identification there is an equivalence of two definitions of derived coisotropic structures in the literature.
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