LAUSR

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.