Surveys in Mathematics and its Applications

ISSN 1842-6298 (electronic), 1843-7265 (print)
 Volume 17 (2022), 397 -- 429

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This work is licensed under a Creative Commons Attribution 4.0 International License.

COMPARISON THEOREMS FOR KAN, FAINTLY UNIVERSAL AND STRONGLY UNIVERSAL DERIVED FUNCTORS

Alisa Govzmann, Damjan Pištalo and Norbert Poncin

Abstract. 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.

2020 Mathematics Subject Classification: 18E35; 18N40; 14A30
Keywords: Localization, model category, homotopy category, derived functor

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Alisa Govzmann
University of Luxembourg,
6, Avenue de la Fonte,
L-4364 Esch-sur-Alzette, Luxemburg.
e-mail: alisa.govzmann@uni.lu


Damjan Pištalo
University of Luxembourg,
6, Avenue de la Fonte,
L-4364 Esch-sur-Alzette, Luxemburg.
e-mail: damjan.pistalo@uni.lu


Norbert Poncin
University of Luxembourg,
6, Avenue de la Fonte,
L-4364 Esch-sur-Alzette, Luxemburg.
e-mail: norbert.poncin@uni.lu


http://www.utgjiu.ro/math/sma