On crossoid structure on knots

We define a structure called crossoid for description of colorings of the crossings in knots diagrams. Crossoids generalize parities in knot theory introduced by V.O. Manturov. On the other hand, any biquandle induces a crossoid structure. We give a topological description of the fundamental crossoid of a knot, and define a crossoid cocycle invariant of knots valued in crossoid cohomology.