  We give a complete account of how soft gluon, massless quark, evolution
equations in colour space originate, from a factorization into a hard cross
section density operator and a soft function encoding measurements and the
projection on definite colours. We detail this formalism up to the two loop
level and we demonstrate how the evolution kernels relate to infrared
subtractions, and how the resolution of infrared singular regions conspires
with the structure of observables the algorithm should be able to predict. The
latter allows us to address evolution in different kinematic variables,
including energy ordering and angular cutoffs in non-global observables. The
soft factor and its evolution resembles a hadronization model including effects
such as colour reconnection, and could give insight into the structure of power
corrections in observables which require soft gluon evolution.
