  A spatial surface is a compact surface embedded in the $3$-sphere. We assume
that each connected component has non-empty boundary. Spatial surfaces are
represented by diagrams of spatial trivalent graphs. In this paper, we
introduce the notion of a groupoid rack, which is an algebraic structure that
can be used for colorings of diagrams of oriented spatial surfaces.
Furthermore, we show that the groupoid rack has a universal property on
colorings for diagrams of spatial surfaces.

Geometric Topology