CAUCHY COMPLETENESS FOR DG-CATEGORIES

被引：0
|
作者：
Nikolic, Branko [1 ]
Street, Ross [1 ]
Tendas, Giacomo [1 ]
机构：
[1] Macquarie Univ, Dept Math & Stat, Ctr Australian Category Theory, N Ryde, NSW 2109, Australia
来源：
THEORY AND APPLICATIONS OF CATEGORIES | 2021年 / 37卷
基金：
澳大利亚研究理事会;
关键词：
chain complex; suspension; mapping cone; differential graded algebra; Cauchy completion; DG-category; absolute colimit; total complex;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：940 / +
页数：25
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