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arXiv · 2508.02612

The derivator of a dg-category

Francesco Genovese·Chiara Sava·Jan Šťovíček
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Abstract

In this work, we construct the stable derivator associated to a homotopically complete and cocomplete dg-category by explicitly defining homotopy Kan extensions via suitable weighted homotopy limits and colimits in dg-categories. By restricting the domain of the derivator to finite direct categories, we obtain a well-defined derivator even for pretriangulated dg-categories. This definition enables an explicit description of the derivator associated to a weakly idempotent complete Frobenius exact category, leading to a more direct characterization in terms of Gorenstein projective (equivalently, Gorenstein injective) diagrams.

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Francesco Genovese, Chiara Sava, Jan Šťovíček. 2025-08-04. The derivator of a dg-category. https://arxiv.org/abs/2508.02612

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