  Reasoning about weak higher categorical structures constitutes a challenging
task, even to the experts. One principal reason is that the language of set
theory is not invariant under the weaker notions of equivalence at play, such
as homotopy equivalence. From this point of view, it is natural to ask for a
different foundational setting which more natively supports these notions.
  Our work takes up on suggestions in the original article arXiv:1705.07442 by
Riehl--Shulman to further develop synthetic $(\infty,1)$-category theory in
simplicial homotopy type theory, including in particular the study of
cocartesian fibrations. Together with a collection of analytic results, notably
due to Riehl--Verity and Rasekh, it follows that our type-theoretic account
constitutes a synthetic theory of fibrations of internal
$(\infty,1)$-categories, w.r.t. to an arbitrary
Grothendieck--Rezk--Lurie-$(\infty,1)$-topos via Shulman's major result
arXiv:1904.07004 about strictification of univalent universes.
