  Consider the intrinsic fundamental group \`a la Grothendieck of a linear
category using connected gradings. In this article we prove that any full
convex subcategory is incompressible, in the sense that the group map between
the corresponding fundamental groups is injective. We start by proving the
functoriality of the intrinsic fundamental group with respect to full
subcategories, based on the study of the restriction of connected gradings.
