论文标题
在生成良好的DG类别的张量产品上
On the tensor product of well generated dg categories
论文作者
论文摘要
我们以满足通用属性的张量产品的张量生成（前修态）的DG类别的同型类别。所得的单体结构是对称的，并且相对于DG类别的相结合rhom（在Toën[26]的意义上）。我们利用增强的衍生的Gabriel-Popescu定理来构建张量产品的构造[21]。 Given a regular cardinal alpha, we define and construct a tensor product of homotopically alpha-cocomplete dg categories and prove that the well generated tensor product of alpha-continuous derived dg categories (in the sense of [21]) is the alpha-continuous dg derived category of the homotopically alpha-cocomplete tensor product.特别是，这表明，良好产生的DG类别的张量产物可保留α-紧凑型。
We endow the homotopy category of well generated (pretriangulated) dg categories with a tensor product satisfying a universal property. The resulting monoidal structure is symmetric and closed with respect to the cocontinuous RHom of dg categories (in the sense of Toën [26]). We give a construction of the tensor product in terms of localisations of dg derived categories, making use of the enhanced derived Gabriel-Popescu theorem [21]. Given a regular cardinal alpha, we define and construct a tensor product of homotopically alpha-cocomplete dg categories and prove that the well generated tensor product of alpha-continuous derived dg categories (in the sense of [21]) is the alpha-continuous dg derived category of the homotopically alpha-cocomplete tensor product. In particular, this shows that the tensor product of well generated dg categories preserves alpha-compactness.
