  We prove that the tree-level scattering amplitudes for (super) Yang-Mills
theory in arbitrary dimensions and for M2-brane models exhibit color-kinematics
(CK) duality. Our proof for Yang-Mills theory substantially simplifies existing
ones in that it relies on the action alone and does not involve any
computation; the proof for M2-brane models establishes this result for the
first time. Explicitly, we combine the facts that Chern-Simons-type theories
naturally come with a kinematic Lie algebra and that both Yang-Mills theory and
M2-brane models are of Chern-Simons form when formulated in pure spinor space,
extending previous work on Yang-Mills currents arXiv:2108.11708. Our
formulation also provides explicit kinematic Lie algebras for the theories
under consideration in the form of diffeomorphisms on pure spinor space. The
pure spinor formulation of CK-duality is based on ordinary, cubic vertices, but
we explain how ordinary CK-duality relates to notions of quartic-vertex 3-Lie
algebra CK-duality for M2-brane models previously discussed in the literature.
