  We derive general conditions for the compatibility of channels in general
probabilistic theory. We introduce formalism that allows us to easily formulate
steering by channels and Bell nonlocality of channels as generalizations of the
well-known concepts of steering by measurements and Bell nonlocality of
measurements. The generalization does not follow the standard line of thinking
stemming from the Einstein-Podolsky-Rosen paradox, but introduces steering and
Bell nonlocality as entanglement-assisted incompatibility tests. We show that
all of the proposed definitions are, in the special case of measurements, the
same as the standard definitions, but not all of the known results for
measurements generalize to channels. For example, we show that for quantum
channels, steering is not a necessary condition for Bell nonlocality. We
further investigate the introduced conditions and concepts in the special case
of quantum theory and we provide many examples to demonstrate these concepts
and their implications.
