MC-biquandles and MC-biquandle coloring quivers (Q6634230)

The article under review introduces mc-biquandles, an algebraic structure designed for telling links apart. An mc-quandle is a set with two intertwined algebraic structures, a biquandle and a birack -- together with intertwining conditions. These intertwining conditions are set in order to comply with the Reidemeister moves of type III applied to neighborhoods where crossings involving strands from the same component coexist with crossings involving strands from different components. Specifically, the biquandle operation is to be used at single component crossings and the birack operation at multi-component crossings. Examples are given where the counting of colorings by mc-biquandles is a stronger invariant than the counting of colorings by biquandles. Furthermore, they categorify the mc-biquandle counting invariant, defining the mc-biquandle coloring quiver.