  Operational contextuality forms a rapidly developing subfield of quantum
information theory. However, the characterization of the quantum mechanical
entities that fuel the phenomenon has remained unknown with many partial
results existing. Here, we present a resolution to this problem by connecting
operational contextuality one-to-one with the no-broadcasting theorem. The
connection works both on the level of full quantum theory and subtheories
thereof. We demonstrate the connection in various relevant cases, showing
especially that for quantum states the possibility of demonstrating
contextuality is exactly characterized by non-commutativity, and for
measurements this is done by a norm-1 property closely related to
repeatability. Moreover, we show how techniques from broadcasting can be used
to simplify known foundational results in contextuality.
