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Aug 5, 2015 at 7:23 comment added Qiaochu Yuan I would say that an abelian category is semisimple if every short exact sequence splits. So I would regard $\text{Vect}$, the abelian category of not-necessarily-finite-dimensional vector spaces, as semisimple. I would also say that an object is semisimple if it's a direct sum, not necessarily finite, of simples.
Aug 4, 2015 at 17:58 vote accept Dyke Acland
Aug 4, 2015 at 17:47 answer added Ehud Meir timeline score: 3
Aug 4, 2015 at 17:41 history asked Dyke Acland CC BY-SA 3.0