Abstract
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 interac-tions between absolute weighted colimits, we also examine the total complex of a chain complex in a DG-category as a non-absolute weighted colimit.
| Original language | English |
|---|---|
| Pages (from-to) | 940-963 |
| Number of pages | 24 |
| Journal | Theory and Applications of Categories |
| Volume | 37 |
| Issue number | 28 |
| Publication status | Published - 7 Aug 2021 |
Keywords
- chain complex
- suspension
- mapping cone
- differential graded algebra
- Cauchy completion
- DG-category
- absolute colimit
- total complex