  The goal of this article is to extend a theorem of Lurie \[
  \mathsf{Sh}_A (X) = \mathsf{Fun}(\mathsf{Exit}_A (X), \mathsf{S}) \]
representing constructible sheaves with values in $ \mathsf{S} $, the $ \infty
$-category of spaces, on a stratified space $ X $ with poset of strata $ A $,
as functors from the exit paths $ \infty $-category $ \mathsf{Exit}_A (X) $ to
$ \mathsf{S} $. Lurie's representation theorem works provided $ A $ satisfy the
ascending chain condition. This typically rules out infinite dimensional
examples of stratified space.
  Building on it and with the help of a stratified homotopy invariance theorem
from Haine, we show that when $ X $ is a nice enough $ A $-stratified space and
when $ A $ is itself stratified $ A_{\leq 0} \subset A_{\leq 1} \subset \cdots
\subset A $ by posets satisfying the ascending chain condition, \[
  \mathsf{Hyp}_A (X) = \mathsf{Fun}(\mathsf{Exit}_A(X), \mathsf{S}) \] the $
\infty $-category of $ A $-constructible hypersheaves on $ X $ is represented
by functors from the exit paths $ \infty $-category of $ X $.
  There are two types of nice stratified spaces on which this extended
representation theorem applies: conically stratified spaces and spaces that are
sequential colimits of conically stratified spaces. Examples of application
include the metric and the topological exponentials of a Fr\'echet manifold,
locally countable simplicial complexes and more generally, locally countable
cylindrically normal CW-complexes.
