  Within the framework of Riehl-Shulman's synthetic $(\infty,1)$-category
theory, we present a theory of two-sided cartesian fibrations. Central results
are several characterizations of the two-sidedness condition \`{a} la
Chevalley, Gray, Street, and Riehl-Verity, a two-sided Yoneda Lemma, as well as
the proof of several closure properties.
  Along the way, we also define and investigate a notion of fibered or sliced
fibration which is used later to develop the two-sided case in a modular
fashion. We also briefly discuss discrete two-sided cartesian fibrations in
this setting, corresponding to $(\infty,1)$-distributors.
  The systematics of our definitions and results closely follows Riehl-Verity's
$\infty$-cosmos theory, but formulated internally to Riehl-Shulman's simplicial
extension of homotopy type theory. All the constructions and proofs in this
framework are by design invariant under homotopy equivalence. Semantically, the
synthetic $(\infty,1)$-categories correspond to internal
$(\infty,1)$-categories implemented as Rezk objects in an arbitrary given
$(\infty,1)$-topos.
