  Quantum instruments describe outcome probability as well as state change
induced by measurement of a quantum system. Incompatibility of two instruments,
i. e. the impossibility to realize them simultaneously on a given quantum
system, generalizes incompatibility of channels and incompatibility of positive
operator-valued measures (POVMs). We derive implications of instrument
compatibility for the induced POVMs and channels. We also study relation of
instrument compatibility to the concept of non-disturbance. Finally, we prove
equivalence between instrument compatibility and postprocessing of certain
instruments, which we term complementary instruments. We illustrate our
findings on examples of various classes of instruments.
