论文标题
DG类别的丰富Koszul二元性
Enriched Koszul duality for dg categories
论文作者
论文摘要
众所周知，小型DG类别DGCAT的类别虽然是单体的，但并未形成单体模型类别。在本文中，我们在尖的弯曲结构的ptdcoa*类别上构建了一个单体模型结构，并表明将其与DGCAT相关的Quillen等效性是单一的。我们还表明，DGCAT是PTDCOA*富集模型类别。结果，DGCAT的同型类别是封闭的单体封闭式，与PTDCOA*的同型类别相同。特别是，这给出了DGCAT中派生的内部HOM的概念构造。作为应用程序，我们在DGCAT中获得了简单映射空间的新描述，并根据Hochschild共同体学组对其同型组进行了计算，重现和略微概括了Toën的众所周知的结果。将我们的方法与toën的方法进行比较，我们还从离散类别的普通神经方面获得了Lurie DG神经的核心的描述。
It is well-known that the category of small dg categories dgCat, though it is monoidal, does not form a monoidal model category. In this paper we construct a monoidal model structure on the category of pointed curved coalgebras ptdCoa* and show that the Quillen equivalence relating it to dgCat is monoidal. We also show that dgCat is a ptdCoa*-enriched model category. As a consequence, the homotopy category of dgCat is closed monoidal and is equivalent as a closed monoidal category to the homotopy category of ptdCoa*. In particular, this gives a conceptual construction of a derived internal hom in dgCat. As an application we obtain a new description of simplicial mapping spaces in dgCat and a calculation of their homotopy groups in terms of Hochschild cohomology groups, reproducing and slightly generalizing well-known results of Toën. Comparing our approach to Toën's, we also obtain a description of the core of Lurie's dg nerve in terms of the ordinary nerve of a discrete category.
