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Hopfological algebra and categorification at a root of unity: the first steps

Mikhail Khovanov
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Abstract

Any finite-dimensional Hopf algebra H is Frobenius and the stable category of H-modules is triangulated monoidal. To H-comodule algebras we assign triangulated module-categories over the stable category of H-modules. These module-categories are generalizations of homotopy and derived categories of modules over a differential graded algebra. We expect that, for suitable H, our construction could be a starting point in the program of categorifying quantum invariants of 3-manifolds.

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Mikhail Khovanov. 2006-03-25. Hopfological algebra and categorification at a root of unity: the first steps. https://arxiv.org/abs/math/0509083

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