Proposition [efr-002X]

Let \mathcal {C} \to B\mathcal {M} be a locally graded category. Then the fiber \mathcal {C}_* over the unique object is equivalent to a 1-category. It consists of those morphisms which go to the identity in B\mathcal {M}, i.e the unit object I \in \mathcal {M}. We call such morphisms unparametrized.