  We consider a general framework for integrable hierarchies in Lax form and
derive certain universal equations from which `functional representations' of
particular hierarchies (like KP, discrete KP, mKP, AKNS), i.e. formulations in
terms of functional equations, are systematically and quite easily obtained.
The formalism genuinely applies to hierarchies where the dependent variables
live in a noncommutative (typically matrix) algebra. The obtained functional
representations can be understood as `noncommutative' analogs of `Fay
identities' for the KP hierarchy.
