  Split opfibrations are functors equipped with a suitable choice of
opcartesian lifts. The purpose of this paper is to characterise internal split
opfibrations through separating the structure of a suitable choice of lifts
from the property of these lifts being opcartesian. The underlying structure of
an internal split opfibration is captured by an internal functor equipped with
an internal cofunctor, while the property may be expressed as a pullback
condition, akin to the simple condition on an internal functor to be an
internal discrete opfibration. Furthermore, this approach provides two
additional characterisations of internal split opfibrations, via the d\'ecalage
construction and strict factorisation systems. For small categories, this
theory clarifies several aspects of delta lenses which arise in computer
science.
