  The geometric Satake correspondence provides an equivalence of categories
between the Satake category of spherical perverse sheaves on the affine
Grassmannian and the category of representations of the dual group. In this
note, we define a combinatorial version of the Satake category using
irreducible components of fibres of the convolution morphism. We then prove an
equivalence of coboundary categories between this combinatorial Satake category
and the category of crystals of the dual group.
