论文标题
在某些确切的单体类别的共同体学上的分级谎言结构
Graded Lie structure on cohomology of some exact monoidal categories
论文作者
论文摘要
对于某些确切的单体类别，我们在单位对象的扩展代数上明确描述了Lie支架的拓扑定义和代数定义之间的联系。由于Schwede和Hermann，拓扑定义涉及扩展类别的循环。代数定义是第一作者，涉及地图的同质升降。由于我们的描述，我们证明了拓扑定义确实在此单体类别设置中产生了Gerstenhaber代数结构。这回答了Hermann的问题，即单位对象具有特定类型的分辨率，称为Power Flat。为了在证明中使用，我们将$ a _ {\ infty} $ - 编码和同型提升技术从Bimodule类别到这些确切的单体类别。
For some exact monoidal categories, we describe explicitly a connection between topological and algebraic definitions of the Lie bracket on the extension algebra of the unit object. The topological definition, due to Schwede and Hermann, involves loops in extension categories. The algebraic definition, due to the first author, involves homotopy liftings of maps. As a consequence of our description, we prove that the topological definition indeed yields a Gerstenhaber algebra structure in this monoidal category setting. This answers a question of Hermann for those exact monoidal categories in which the unit object has a particular type of resolution that is called power flat. For use in proofs, we generalize $A_{\infty}$-coderivation and homotopy lifting techniques from bimodule categories to these exact monoidal categories.
