  We show that there exists a representation of a matrix valued gauge field via
intrinsic "BRST" operator assigned to matrix valued generators of a gauge
algebra. In this way, we reproduce the standard formulation of the ordinary
Yang - Mills theory. In the case of a generating quasigroup/groupoid, we give a
natural counterpart to the Yang - Mills action. The latter counterpart does
also apply as to the most general case of an involution for matrix-valued gauge
generators.
