  We construct a machine which takes as input a locally small symmetric closed
complete multicategory $\mathsf V$. And its output is again a locally small
symmetric closed complete multicategory $\mathsf V\text-\mathcal{C}at$, the
multicategory of small $\mathsf V$-categories and multi-entry $\mathsf
V$-functors.
  An example of such $\mathsf V$ is provided by short spaces (vector spaces
with a system of seminorms) and short maps. When the ground multicategory
$\mathsf V$ is $\mathsf{Set}$ we obtain strict 2-categories and their
surroundings by iterating twice the construction of categories.
