  A tangent category is a categorical abstraction of the tangent bundle
construction for smooth manifolds. In that context, Cockett and Cruttwell
develop the notion of differential bundle which, by work of MacAdam,
generalizes the notion of smooth vector bundle to the abstract setting. Here we
provide a new characterization of those differential bundles and show that, up
to isomorphism, a differential bundle is determined by its projection map and
zero section. We show how these results can be used to quickly identify
differential bundles in various tangent categories.
