T-0-reflection and injective hulls of fibre spaces

We give a characterization of injective (with respect to the class of embeddings) topological fibre spaces using their To-reflection, that turns out to be injective itself. We then prove that the existence of an injective hull of (X, f) in the category Top/B of topological fibre spaces is equivalent to the existence of an injective hull of its T-0-reflection (X-0, f(0)) in Top/B-0 (and in the category Top(0)/B-0 of T-0 topological fibre spaces).