论文标题
局部可呈现的线性类别，Grothendieck类别及其张量产品的过滤双色映射介绍
Filtered bicolimit presentations of locally presentable linear categories, Grothendieck categories and their tensor products
论文作者
论文摘要
我们研究了两种不同的方法，将grothendieck类别恢复为小型类别的过滤二色，以及两者与Grothendieck类别的张量产品的兼容性。首先，我们表明，任何本地提供的线性类别（尤其是任何Grothendieck类别）都可以作为其$α$ ablesublable的对象的子类别的过滤二维型，其中$α$在小规则的基数的家族中有所不同。然后，我们证明，可以将本地可呈现的线性类别的张量产品（尤其是Grothendieck类别的张量产物）作为$α$ coctote-copterete线性类别的$α$ -presentable对象的相应子类别的$α$ coctote线性类别的kelly张量产品的过滤双胶片恢复。其次，我们表明，可以将任何Grothendieck类别恢复为其线性位点演示的过滤双胶体。然后，我们证明，与第一种情况相反，Grothendieck类别的张量产品通常无法作为相应线性位点的张量产物的过滤双胶片回收。最后，作为第一个演示文稿的直接应用，我们将$α$ - 重合的线性类别的凯利张量产品的功能性，关联性和对称性转化为局部可呈现的线性类别的张量。
We investigate two different ways of recovering a Grothendieck category as a filtered bicolimit of small categories and the compatibility of both with the tensor product of Grothendieck categories. Firstly, we show that any locally presentable linear category (and in particular any Grothendieck category) can be recovered as the filtered bicolimit of its subcategories of $α$-presentable objects, with $α$ varying in the family of small regular cardinals. We then prove that the tensor product of locally presentable linear categories (and in particular the tensor product of Grothendieck categories) can be recovered as a filtered bicolimit of the Kelly tensor product of $α$-cocomplete linear categories of the corresponding subcategories of $α$-presentable objects. Secondly, we show that one can recover any Grothendieck category as a filtered bicolimit of its linear site presentations. We then prove that the tensor product of Grothendieck categories, in contrast with the first case, cannot be recovered in general as a filtered bicolimit of the tensor product of the corresponding linear sites. Finally, as a direct application of the first presentation, we translate the functoriality, associativity and symmetry of the Kelly tensor product of $α$-cocomplete linear categories to the tensor product of locally presentable linear categories.
