Enriched categories as a free cocompletion

This paper has two objectives. The first is to develop the theory of bicategories enriched in a monoidal bicategory—categorifying the classical theory of categories enriched in a monoidal category—up to a description of the free cocompletion of an enriched bicategory under a class of weighted bicolimits. The second objective is to describe a universal property of the process assigning to a monoidal category VV the equipment of VV-enriched categories, functors, transformations, and modules; we do so by considering, more generally, the assignation sending an equipment CC to the equipment of CC-enriched categories, functors, transformations, and modules, and exhibiting this as the free cocompletion of a certain kind of enriched bicategory under a certain class of weighted bicolimits.