  We define and study notions of comprehension in $(\infty,1)$-category theory.
In essence, we do so by implementing B\'{e}nabou's foundations of naive
category theory in a univalent meta-theory. In particular, we develop natural
generalizations of smallness and relative definability in this context, and
show for instance that the universal cartesian fibration is small. Furthermore,
by building on Johnstone's notion of comprehension schemes for ordinary fibered
categories, we characterize and relate numerous higher categorical properties
and structures such as left exactness, local cartesian closedness, univalent
morphisms and internal $(\infty,1)$-categories in terms of comprehension
schemes.
