  We clarify the derivation of high-energy QCD evolution equations from the
fundamental gauge symmetry of QCD. The gauge-fixed classical action of the
Color Glass Condensate (CGC) is shown to be invariant under a suitable BRST
symmetry, that holds after the separation of the gluon modes into their fast
classical (background) part, the soft component and the semifast one, over
which the one-step quantum evolution is carried out. The resulting
Slavnov-Taylor (ST) identity holds to all orders in perturbation theory and
strongly constrains the CGC effective field theory (EFT) arising from the
integration of the soft modes. We show that the ST identity guarantees
gauge-invariance of the EFT. It also allows to control the dependence on the
gauge-fixing choice for the semifast modes (usually the lightcone gauge in
explicit computations). The formal properties of the evolution equations valid
in different regimes (BKFL, JIMWLK, ...) can be all derived in a unified
setting within this algebraic approach.
