  Given a Legendrian knot in $(\mathbb{R}^3, \ker(dz-ydx))$ one can assign a
combinatorial invariants called ruling polynomials. These invariants have been
shown to recover not only a (normalized) count of augmentations but are also
closely related to a categorical count of augmentations in the form of the
homotopy cardinality of the augmentation category. In this article, we prove
that that the homotopy cardinality of the $n$-dimensional representation
category is a multiple of the $n$-colored ruling polynomial. Along the way, we
establish that two $n$-dimensional representations are equivalent in the
representation category if they are conjugate DGA homotopic. We also provide
some applications to Lagrangian concordance.
