Framed bicategories and monoidal fibrations

Understand

In some bicategories, the 1-cells are `morphisms' between the 0-cells, such as functors between categories, but in others they are `objects' over the 0-cells, such as bimodules, spans, distributors, or parametrized spectra.

• Many bicategorical notions do not work well in these cases, because the `morphisms between 0-cells', such as ring homomorphisms, are missing.
• We can include them by using a pseudo double category, but usually these morphisms also induce base change functors acting on the 1-cells.
• We avoid complicated coherence problems by describing base change `nonalgebraically', using categorical fibrations.