Want to take part in these discussions? Sign in if you have an account, or apply for one below
Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.
I was dissatisfied with the discussion at semisimple category because it only defined a semisimple monoidal Vect-enriched category, completely ignoring the more common notion of semsimple abelian category.
So, I stuck in the definition of semisimple abelian category.
However, I still think there is a lot that could be improved here: when is a semisimple abelian category which is also monoidal a semsimple monoidal category in some sense like that espoused here???
I think this article is currently a bit under the sway of Bruce Bartlett’s desire to avoid abelian categories. This could be good in some contexts, but not necessarily in all!
We don’t hear a lot from Bruce here, so I’m wondering who was under his sway… :-) Why does Bruce desire to avoid abelian categories?
The article was under Bruce’s sway. He explains there why he wants to avoid abelian categories, but I sympathize too little to try to convey his point. I guess he’s trying to say that for semisimple categories, all that really matters are biproducts and splitting idempotents. Sounds vaguely familiar, eh? But I’m still not sure I agree…
The second definition of semisimple category on this page is as a “monoidal linear category” with certain properties. But none of the properties or any of the later discussion on this page uses the monoidal structure, nor is it very consistent with the first defintion (as a semisimple abelian category, which makes no reference to monoidality).
1 to 8 of 8