  An answer to the question investigated in this paper brings a new
characterization of internal groupoids such that: (a) it holds even when finite
limits are not assumed to exist; (b) it is a full subcategory of the category
of involutive-2-links, that is, a category whose objects are morphisms equipped
with a pair of interlinked involutions. This result highlights the fact that
even thought internal groupoids are internal categories equipped with an
involution, they can equivalently be seen as tri-graphs with an involution.
Moreover, the structure of a tri-graph with an involution can be further
contracted into a simpler structure consisting of one morphism with two
interlinked involutions. This approach highly contrasts with the one where
groupoids are seen as reflexive graphs on which a multiplicative structure is
defined with inverses.
