  We use the complete Segal approach to the theory of Cartesian fibrations to
define and study representable Cartesian fibrations, generalizing representable
right fibrations which have played a key role in $\infty$-category theory. In
particular, we give a construction of representable Cartesian fibrations using
over-categories and prove the Yoneda lemma for representable Cartesian
fibration, which generalizes the established Yoneda lemma for right fibrations.
  We then use the theory of Cartesian fibrations to study complete Segal
objects internal to an $\infty$-category. Concretely, we prove the {\it
fundamental theorem of complete Segal objects}, which characterizes
equivalences of complete Segal objects. Finally we give two application of the
results. First, we present a method to construct Segal objects and second we
study the representability of the universal coCartesian fibration.
