  We consider a generic Metric-Affine Cosmological setup and classify some
particularly interesting specific cases of Perfect Hyperfluids. In particular,
we present the form of conservation laws for the cases of pure spin, pure
dilation and pure shear fluids. We also develop the concept of an
incompressible hyperfluid and pay special attention to the case of a
hypermomentum preserving hyperfluid. We also give a specific example on the
emergence of the spin, dilation and shear currents through matter-connection
couplings. In addition, starting from the generalized acceleration equation for
the scale factor including torsion and non-metricity we provide a first
integral of motion relating the latter with the rest of the hyperfluid
variables. These results then formalize the analysis of the non-Riemannian
effects in Cosmology.
