  We define the notion of an indexed profunctor over a 2-category, and use it
to develop an abstract theory of limits. The theory subsumes (conical) limits,
weighted limits, ends and Kan extensions. Results include an abstract version
of the theorem that right adjoint functors preserve limits, and an abstract
account of the phenomenon that the comparison arrow implicated in the
preservation of a limit by a functor is natural in any functorial variable the
functor happens to depend on. These results make an extensive use of the data
and axioms of an indexed profunctor over a 2-category.
