<p style='text-indent:20px;'>We introduce Poisson double algebroids, and the equivalent concept of double Lie bialgebroid, which arise as second-order infinitesimal counterparts of Poisson double groupoids. We develop their underlying Lie theory, showing how these objects are related by differentiation and integration. We use these results to revisit Lie 2-bialgebras by means of Poisson double structures.</p>

中文翻译：

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泊松双结构

<p style='text-indent:20px;'>我们引入了泊松双代数，以及双李双代数的等价概念，它们是泊松双群的二阶无穷小对应物。我们发展了他们的基本谎言理论，展示了这些对象如何通过微分和整合相关联。我们利用这些结果通过 Poisson 双结构重新审视了李 2-双代数。</p>