Projects per year
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 |
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Pages (from-to) | 940-963 |
Number of pages | 24 |
Journal | Theory and Applications of Categories |
Volume | 37 |
Issue number | 28 |
Publication status | Published - 2021 |
Keywords
- chain complex
- suspension
- mapping cone
- dierential graded algebra
- Cauchy completion
- DG-category
- absolute colimit
- total complex
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Dive into the research topics of 'Cauchy completeness for DG-categories'. Together they form a unique fingerprint.Projects
- 2 Finished
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Working synthetically in higher categorical structures
Lack, S., Verity, D., Garner, R. & Street, R.
19/06/19 → 18/06/22
Project: Other
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Monoidal categories and beyond: new contexts and new applications
Street, R., Verity, D., Lack, S., Garner, R. & MQRES Inter Tuition Fee only, M. I. T. F. O.
30/06/16 → 17/06/19
Project: Research