  This is the second paper that completes the series started by \cite{Fem}. In
the former, we constructed a tricategory $\DblPs$ of double categories and
announced the notion of categories internal in tricategories of the type of
$\DblPs$, as alternative to the notion of intercategories of Grandis and
Par\'e, so that monoids from \cite{Gabi} fit as their particular case. We
complete this project in the current paper and show that weak pseudomonoids in
a tricategory which has B\"ohm's monoidal category as the underlying 1-category
are internal categories in $\DblPs$. Moreover, we prove that categories
enriched over certain type of tricategories may be made categories internal in
them, and show how the tricategory of tensor categories is an example of this
over the ambient tricategory $2\x\Cat_{wk}$ of 2-categories, pseudofunctors,
pseudonatural transformations and modifications.
