  In flat space, the color/kinematics duality states that perturbative
Yang-Mills amplitudes can be written in such a way that kinematic numerators
obey the same Jacobi relations as their color factors. This remarkable duality
implies BCJ relations for Yang-Mills amplitudes and underlies the double copy
to gravitational amplitudes. In this paper, we find analogous relations for
Yang-Mills amplitudes in AdS$_4$. In particular we show that the kinematic
numerators of 4-point Yang-Mills amplitudes computed via Witten diagrams in
momentum space enjoy a generalised gauge symmetry which can be used to enforce
the kinematic Jacobi relation away from the flat space limit, and we derive
deformed BCJ relations which reduce to the standard ones in the flat space
limit. We illustrate these results using compact new expressions for 4-point
Yang-Mills amplitudes in AdS$_4$ and their kinematic numerators in terms of
spinors. We also spell out the relation to 3d conformal correlators in momentum
space, and speculate on the double copy to graviton amplitudes in AdS$_4$.
