finite abelian category

Finite abelian categories



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 said to be 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.


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