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We develop a new description of the much-studied $\kappa$-Minkowskinoncommutative spacetime, centered on representing on a single Hilbert spacenot only the $\kappa$-Minkowski coordinates, but also the associateddifferential calculus and the $\kappa$-Poincar\'e symmetry generators.  In this "pregeometric" representation the relevant operators act on thekinematical Hilbert space of the covariant formulation of quantum mechanics,which we argue is the natural framework for studying the implications of thestep from commuting spacetime coordinates to the $\kappa$-Minkowski case, wherethe spatial coordinates do not commute with the time coordinate. Theempowerment provided by this kinematical-Hilbert space representation allows usto give a crisp characterization of the "fuzziness" of $\kappa$-Minkowskispacetime, whose most striking aspect is a relativity of spacetime locality. Weshow that relative locality, which had been previously formulated exclusivelyin classical-spacetime setups, for a quantum spacetime takes the shape of adependence of the fuzziness of a spacetime point on the distance at which anobserver infers properties of the event that marks the point.

Relative locality in a quantum spacetime and the pregeometry of $\kappa$-Minkowski