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Nov 3 at 23:34 comment added Algeboy Ben Webster's clearly thinking along the same lines. However abelian categories need not be module categories. Module categories have much beyond that. I simply meant to point out what additional qualities are defining of module categories.
Nov 2 at 21:14 comment added R. van Dobben de Bruyn Isn't the observation that two groups with the same number of irreducible representations give isomorphic module categories a long-winded version of Ben Webster's answer? The dimension of matrix algebras you get is irrelevant as they are all Morita equivalent.
S Sep 13 at 2:38 review First answers
Sep 13 at 2:51
S Sep 13 at 2:38 history edited Algeboy CC BY-SA 4.0
Hecke -> Hopf, a classic typo of mine.
Sep 12 at 21:45 history edited LSpice CC BY-SA 4.0
Typo; displaying displayed equations
S Sep 12 at 21:02 review First answers
Sep 12 at 23:56
S Sep 12 at 21:02 history answered Algeboy CC BY-SA 4.0