  It is well known that to give an oplax functor of bicategories
$\mathbf{1}\to\mathscr{C}$ is to give a comonad in $\mathscr{C}$. Here we
generalize this fact, replacing the terminal bicategory by any bicategory
$\mathscr{A}$ for which the composition functor admits generic factorisations.
We call bicategories with this property generic, and show that for generic
bicategories $\mathscr{A}$ one may express the data of an oplax functor
$\mathscr{A}\to\mathscr{C}$ much like the data of a comonad; the main advantage
of this description being that it does not directly involve composition in
$\mathscr{A}$.
  We then go on to apply this result to some well known bicategories, such as
cartesian monoidal categories (seen as one object bicategories), bicategories
of spans, and bicategories of polynomials with cartesian 2-cells.
