As the question was originally about internal enriched categories I want to add the following easy observation. If the fibration U : UU -> BB is *locally small* and C is a U-enriched fibration over BB (as defined in Gouzou & Grunig) then the associated (non-enriched) fibration over BB is small (i.e. the externalisation of an internal category). The family of morphisms of this internal category is given by hom(I_{C_0 x C_0},H) : C_1 ---> C_0 x C_0 where hom comes from U being locally small. Thomas