  Regardless of its environment, the category of internal groupoids is shown to
be equivalent to the full subcategory of involutive-2-links that are unital and
associative. The new notion of involutive-2-link originates from the study of
triangulated surfaces and their application in additive manufacturing and
3d-printing. Thus, this result establishes a bridge between the structure of an
internal groupoid and an abstract triangulated surface. An example is provided
which can be thought of as a crossed-module of magmas rather than groups.
