论文标题
DG类别的Cauchy完整性
Cauchy completeness for DG-categories
论文作者
论文摘要
我们回到富含链复合物的丰富类别理论和研究类别的根源。也就是说，我们处理差异分类类别（简称DG类别）。特别是，我们回想起加权的colimit并提供例子。我们解决了如何根据某些特定有限的绝对colimits的存在来表征Cauchy完整的DG类别的50年历史的问题。除了绝对加权的colimits之间的相互作用外，我们还研究了DG类别中链复合物的总复合物作为非充血性加权colimit。
We go back to the roots of enriched category theory and study categories enriched in chain complexes; that is, we deal with differential graded categories (DG-categories for short). In particular, we recall weighted colimits and provide examples. We solve the 50 year old question of how to characterize Cauchy complete DG-categories in terms of existence of some specific finite absolute colimits. As well as the interactions between absolute weighted colimits, we also examine the total complex of a chain complex in a DG-category as a non-absolute weighted colimit.
