  Algebraic structures involving both multiplications and comultiplications
(such as, e.g., bialgebras or Hopf algebras) can be encoded using PROPs
(categories with PROducts and Permutations) of Adams and MacLane. To encode
such structures on objects of a braided monoidal category, we need PROBs
(braided analogs of PROPs). Colored PROBs correspond to multi-sorted
structures.
  In particular, we have a colored PROB B governing non-negatively graded
bialgebras in braided categories. As a category, B splits into blocks B_n
according to the grading. We relate B_n with the category P_n of perverse
sheaves on the n-th symmetric product of the complex line, smooth with respect
to the natural stratification by multiplicities. More precisely, we show that
P_n is equivalent to the category of functors from B_n to vector spaces. This
gives a natural quiver description of P_n.
