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 [32]). 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 [27]. Given a regular cardinal α, we define and construct a tensor product of homotopically α-cocomplete dg categories and prove that the well generated tensor product of α-continuous derived dg categories (in the sense of [27]) is the α-continuous dg derived category of the homotopically α-cocomplete tensor product. In particular, this shows that the tensor product of well generated dg categories preserves α-compactness.

我们赋予生成良好的（预三角化的）dg 类别的同伦类别一个满足通用性质的张量积。由此产生的幺半群结构关于 dg 类别的共连续 RHom 是对称和封闭的（在 Toën [32]的意义上）。我们利用增强的 Gabriel-Popescu 定理 [27]，根据 dg 派生类别的本地化给出了张量积的构造。给定规则的基数α，我们定义并构建同伦的张量积α -cocomplete DG类别和证明的阱生成张量积α -Continuous衍生DG类别（在[27]的意义上）是α -连续分克同伦的派生范畴α -cocomplete 张量积。特别是，这表明生成良好的 dg 类别的张量积保留了α -紧凑性。