  Yang-Mills gauge theory on Minkowski space supports a
Batalin-Vilkovisky-infinity algebra structure, all whose operations are local.
To make this work, the axioms for a BV-infinity algebra are deformed by a
quadratic element, here the Minkowski wave operator. This homotopy structure
implies BCJ/color-kinematics duality; a cobar construction yields a strict
algebraic structure whose Feynman expansion for Yang-Mills tree amplitudes
complies with the duality. It comes with a `syntactic kinematic algebra'.
