nLab
finite abelian category

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 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.

Reference

Last revised on November 4, 2016 at 06:53:32. See the history of this page for a list of all contributions to it.