nLab finite abelian category

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Finite abelian categories

Finite abelian categories

Definition

Definition

Let kk be a field, and let 𝒞\mathcal{C} be a kk-linear abelian category (i.e. one whose Ab-enrichment is lifted to a Vect-enrichment). Then 𝒞\mathcal{C} is called [Etingof & Ostrik 2003 p. 3] finite (over kk) if

Theorem (Deligne)

For any finite abelian category CC, there exists a finite-dimensional kk-algebra AA and an kk-linear equivalence between CC and AA-Mod fdMod_{fd}, the category of modules over AA that are finite-dimensional as vector spaces over kk.

References

Last revised on September 1, 2023 at 09:24:13. See the history of this page for a list of all contributions to it.