  We categorify cocompleteness results of monad theory, in the context of
pseudomonads. We first prove a general result establishing that, in any
2-category, weighted bicolimits can be constructed from oplax bicolimits and
bicoequalizers of codescent objects. After prerequisites on pseudomonads and
their pseudo-algebras, we give a 2-dimensional Linton theorem reducing
bicocompleteness of 2-categories of pseudo-algebras to existence of
bicoequalizers of codescent objects. Finally we prove this condition to be
fulfilled in the case of a bifinitary pseudomonad, ensuring bicocompleteness.
