  We describe a categorical g action, called a (g,theta) action, which is
easier to check in practice. Most categorical g actions can be shown to be of
this form. The main result is that a (g,theta) action carries actions of quiver
Hecke algebras (KLR algebras). We discuss applications of this fact to
categorical vertex operators, affine Grassmannians (or Nakajima quiver
varieties) and to homological knot invariants.
