Building on the notion of metric hypersurface data in the null case, we introduce a geometry on a manifold endowed with a degenerate metric of signature $\{0, +, \cdots, +\}$. Such space admits a uniquely defined family of connections related to each other by a group of transformations. We then incorporate a notion of extrinsic curvature and define the so-called constraint tensor. This abstract null geometry is adequate to describe null hypersurfaces in a spacetime from a completely detached point of view. We describe two applications, one in the context of degenerate horizons and the other concerning the characteristic initial value problem of the Einstein field equations.