Given an algebraically closed field $k$ and a Noetherian commutative $k$-algebra $A$, all simple modules over $A$ are 1-dimensional - What is the analogous statement for symmetric monoidal $k$-linear categories? - What is the analogous statement for braided monoidal $k$-linear categories? We can assume the category is Abelian and the product functor is right exact in both variables I expect something of the sort "any module category is equivalent to $Vect$", although I don't know what's the analogue of "Noetherian" and (what's troubling me the most) I have no idea how braided and symmetric are different in this repsect