  We study the category of G(O)-equivariant perverse coherent sheaves on the
affine Grassmannian of G. This coherent Satake category is not semisimple and
its convolution product is not symmetric, in contrast with the usual
constructible Satake category. Instead, we use the Beilinson-Drinfeld
Grassmannian to construct renormalized r-matrices. These are canonical nonzero
maps between convolution products which satisfy axioms weaker than those of a
braiding.
  We also show that the coherent Satake category is rigid, and that together
these results strongly constrain its convolution structure. In particular, they
can be used to deduce the existence of (categorified) cluster structures. We
study the case G = GL_n in detail and prove that the loop rotation equivariant
coherent Satake category of GL_n is a monoidal categorification of an explicit
quantum cluster algebra.
  More generally, we construct renormalized r-matrices in any monoidal category
whose product is compatible with an auxiliary chiral category, and explain how
the appearance of cluster algebras in 4d N=2 field theory may be understood
from this point of view.
