论文标题
弯曲的操作演算
Curved operadic calculus
论文作者
论文摘要
弯曲的代数是差分级代数的概括，最近发现了许多应用。这本基本文章的目的是介绍弯曲的曲目的概念，并在此新层面上开发出口表明。弯曲的操作演算的代数侧为我们提供了通用的构造：使用弯曲的操作双模模的新概念，我们构建了弯曲的通用包围代数。由于在弯曲的上下文中没有准同态的概念，因此我们使用新方法开发了弯曲作战的同义理论。 This approach leads us to introduce the new notion of a curved absolute operad, which is the notion Koszul dual to counital cooperads non-necessarily conilpotent, and we construct a complete Bar-Cobar adjunction between them.我们赋予了合适的模型类别结构的绝对曲线。我们建立了二元函数的双重平方，该平方与Unital Operad和coniltertent弯曲的Cooperads之间的条形obobar辅助交织在一起。这使我们能够为各种弯曲的绝对作业计算最小的同事分辨率。使用完整的条形结构，我们显示了用于弯曲代数的一般同质转移定理。在此过程中，我们构建了非必要的Cofree Cooperad。
Curved algebras are a generalization of differential graded algebras which have found numerous applications recently. The goal of this foundational article is to introduce the notion of a curved operad, and to develop the operadic calculus at this new level. The algebraic side of the curved operadic calculus provides us with universal constructions: using a new notion of curved operadic bimodules, we construct curved universal enveloping algebras. Since there is no notion of quasi-isomorphism in the curved context, we develop the homotopy theory of curved operads using new methods. This approach leads us to introduce the new notion of a curved absolute operad, which is the notion Koszul dual to counital cooperads non-necessarily conilpotent, and we construct a complete Bar-Cobar adjunction between them. We endow curved absolute operads with a suitable model category structure. We establish a duality square of duality functors which intertwines this complete Bar-Cobar construction with the Bar-Cobar adjunction between unital operads and conilpotent curved cooperads. This allows us to compute minimal cofibrant resolutions for various curved absolute operads. Using the complete Bar construction, we show a general Homotopy Transfer Theorem for curved algebras. Along the way, we construct the non-necessarily conilpotent cofree cooperad.
