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<p>We give a purely derivator-theoretical reformulation and proof of a classic result of Happel and Ladkani, showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence provides a bridge between homotopy theory and representation theory: indeed, our result is a derivator-theoretic version of the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\infty \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>∞</mi> </math></EquationSource> </InlineEquation>-Dold-Kan correspondence for bounded chain complexes. Moreover, our equivalence can also be realized as an action of a spectral bimodule in the setting of universal tilting theory developed by Groth and Šťovíček.</p>

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\(\infty \)-Dold-Kan Correspondence via Representation Theory

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  • 发表日期：

    2026年3月26日

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  • Chiara Sava

摘要

We give a purely derivator-theoretical reformulation and proof of a classic result of Happel and Ladkani, showing that it occurs uniformly across stable derivators and it is then independent of coefficients. The resulting equivalence provides a bridge between homotopy theory and representation theory: indeed, our result is a derivator-theoretic version of the \(\infty \) ∞ -Dold-Kan correspondence for bounded chain complexes. Moreover, our equivalence can also be realized as an action of a spectral bimodule in the setting of universal tilting theory developed by Groth and Šťovíček.