  In this paper, we develop the notion of presentability in the parametrised
homotopy theory framework of Barwick-Dotto-Glasman-Nardin-Shah over orbital
categories. We formulate and prove a characterisation of parametrised
presentable categories in terms of its associated straightening. From this we
deduce a parametrised adjoint functor theorem from the unparametrised version,
prove various localisation results, and we record the interactions of the
notion of presentability here with multiplicative matters. Such a theory is of
interest for example in equivariant homotopy theory, and we will apply it in a
companion work to construct the category of parametrised noncommutative motives
for equivariant algebraic K-theory.
