  Let $G$ be a semisimple simply-connected algebraic group over an
algebraically closed field of characteristic zero. We prove that the affine
Hecke category associated to the loop group of $G$ is equivalent to the
colimit, evaluated in the $\infty$-category of monoidal stable
$\infty$-categories, of the finite type Hecke subcategories associated to
standard parahoric subgroups. The main ingredient is an inductive
characterization of colimits indexed by (sufficiently nice) bistratified
categories. Our method is very general and can be used to prove a number of
analogous 'colimit theorems,' e.g. for D-modules on the loop group.
