论文标题
同质字符作为同质限制
Homotopy characters as a homotopy limit
论文作者
论文摘要
对于对应于派生的代数群的HOPF DG-Algebra，我们计算了分类空间构建给出的DG-Elgebras相关cosimimplicial系统的同层限制。同质限制在DG类别的模型类别中采用。生成的DG类别的对象是$ \ operatotorName {Cobar}（a）$的Maurer-Cartan元素，或一二维$ a_ \ iffty $ comcomodules a $ a $ a $。这些可以将其视为与相应派生组的同质性的字符。它们的张量产品是根据Kadeishvili的乘积来解释的。我们还研究了此DG类别的DG模型的编码类别。
For a Hopf DG-algebra corresponding to a derived algebraic group, we compute the homotopy limit of the associated cosimplicial system of DG-algebras given by the classifying space construction. The homotopy limit is taken in the model category of DG-categories. The objects of the resulting DG-category are Maurer-Cartan elements of $\operatorname{Cobar}(A)$, or 1-dimensional $A_\infty$-comodules over $A$. These can be viewed as characters up to homotopy of the corresponding derived group. Their tensor product is interpreted in terms of Kadeishvili's multibraces. We also study the coderived category of DG-modules over this DG-category.
