The derivative of global surface-holonomy for a non-abelian gerbe

Starting with a non-abelian gerbe represented by differential cocycle, values in given crossed-module, this paper explicitly calculates formula for the derivative of associated surface holonomy squares mapped into base manifold; spheres later considered as special case. While definitions used gerbes, their connections, and induced will initially be simplicial, translations cubical setting provided to aide explicit coordinate-based calculations. there are many previously published results on properties these including some calculations over single open set, endeavors take local glue them together across multiple sets order obtain expression change respect one-parameter family squares.