Comparison theorems for Kan, faintly universal and strongly universal derived functors
We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors that are considered in the literature. More precisely, we show that Kan and faint derived functors coincide when we use...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
University Constantin Brancusi of Targu-Jiu
2022-12-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | https://www.utgjiu.ro/math/sma/v17/p17_20.pdf |
| Summary: | We distinguish between faint, weak, strong and strict localizations of categories at morphism families and show that this framework captures the different types of derived functors that are considered in the literature. More precisely, we show that Kan and faint derived functors coincide when we use the classical Kan homotopy category, and when we use the Quillen homotopy category, Kan and strong derived functors coincide. Our comparison results are based on the fact that the Kan homotopy category is a weak localization and that the Quillen homotopy category is a strict localization. |
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| ISSN: | 1843-7265 1842-6298 |