A quantum arrow usually cannot be written as a product of a co-point and a point. One can think of it as a superposition of classical directed edges of a graph. There is a natural operation multiplying arrows by points and arrows by arrows represented by ordinary matrix multiplication. The reverse of a quantum arrow is found by taking the Hermitian conjugate of its matrix. A Hermitian arrow is one that is its own reverse.
Reversal is a basis independent property of an arrow.
Another important type of arrow is a unitary arrow which is represented by a unitary matrix. A unitary arrow may be used to carry out a change of basis on the point space. The property of being unitary is also basis independent. A quantum graph is an element of the Grassmann algebra over the space of arrows. The basis for the space of quantum graphs is the Grassmann product of a number of basis elements of the space of arrows.