论文标题
模块化的作业是鲍尔·鲍拉德（Brauer Poserad）上的模块
Modular operads as modules over the Brauer properad
论文作者
论文摘要
我们表明，模块化的作业等同于我们称为Brauer Porporad的某个简单的Poherad上的模块。此外，我们表明，在这种情况下，Feynman变换对应于此类模块的Cobar Construction。为了确切地说，我们将钢筋和筒子构造的机械扩展到扭曲的形态上，以延伸到一般的适当的模块。这将代数的经典案例推广到了一家奥尔塔尔，并且可能具有独立的利益。作为应用程序，我们为模块化攻击绘制了Koszul二重性理论。
We show that modular operads are equivalent to modules over a certain simple properad which we call the Brauer properad. Furthermore, we show that, in this setting, the Feynman transform corresponds to the cobar construction for modules of this kind. To make this precise, we extend the machinery of the bar and cobar constructions relative to a twisting morphism to modules over a general properad. This generalizes the classical case of algebras over an operad and might be of independent interest. As an application, we sketch a Koszul duality theory for modular operads.
