  Quantum Darwinism proposes that the proliferation of redundant information
plays a major role in the emergence of objectivity out of the quantum world. Is
this kind of objectivity necessarily classical? We show that if one takes
Spekkens' notion of noncontextuality as the notion of classicality and the
approach of Brand\~{a}o, Piani and Horodecki to quantum Darwinism, the answer
to the above question is `yes', if the environment encodes sufficiently well
the proliferated information. Moreover, we propose a threshold on this
encoding, above which one can unambiguously say that classical objectivity has
emerged under quantum Darwinism.
