Incompatibility in quantum theory and other operational theories

Two things can be called incompatible if they are not consistent with each other. In the context of a physical theory, two devices, A and B, described by the theory are called incompatible if the theory does not allow for the existence of a third device C that would have both A and B as its components.  Incompatibility is a fascinating aspect of many physical theories, especially in the case of quantum theory. The concept of incompatibility gives a common ground for several famous impossibility statements within quantum theory, such as 'no-cloning' and 'no information without disturbance'; these can be all seen as statements about incompatibility of certain devices. In this talk we formulate incompatibility in a general form and demonstrate its various aspects.