Abstract
We show that a version of the cube axiom holds in cosimplicial unstable coalgebras and cosimplicial spaces equipped with a resolution model structure. As an application, classical theorems in unstable homotopy theory are extended to this context.
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Acknowledgments
I would like to thank Hadrian Heine and Markus Spitzweck for patiently answering my questions on ∞-categorical issues. Finally, I thank the Deutsche Forschungsgemeinschaft for support through the Schwerpunktprogramm 1786 “Homotopy theory and algebraic geometry”.
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Stelzer, M. The cube axiom and resolutions in homotopy theory. Isr. J. Math. 261, 395–417 (2024). https://doi.org/10.1007/s11856-023-2582-9
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DOI: https://doi.org/10.1007/s11856-023-2582-9