  We give a new, fully mathematical, construction of the space of local
operators in the holomorphic-topological twist of 4d $\mathcal N=2$ gauge
theories. It is based on computations of morphism spaces in the DG category of
line operators, which (by work of Kapustin-Saulina and Cautis-Williams) may be
represented as ind-coherent sheaves on the affine Grassmannian and, more
generally, on the $\mathcal R_{G,N}$ spaces of Braverman-Finkelberg-Nakajima.
We prove that characters of our morphisms spaces reproduce the Schur indices of
4d $\mathcal N=2$ theories, and that the spaces themselves agree with the 4d
$\mathcal N=2$ vertex algebras of Beem-Lemos-Liendo-Peelaers-Rastelli-Van Rees,
Oh-Yagi, Butson and Jeong. We also generalize our construction to local
operators at junctions of Wilson-'t Hooft lines, and compare the Euler
character of the morphism spaces to the Schur indices in the work of
Cordova-Gaiotto-Shao.
