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

从以非阿贝尔微分cocycle表示的非阿贝尔gerbe开始，以给定的交叉模块中的值开始，本文显式地计算映射到基本流形中的正方形的相关表面完整性的导数的公式；球体后来被视为特例。尽管本文中用于gerbes的定义，它们的联系和诱导的完整性最初是简单的，但将提供转换为立方设置以帮助基于显式坐标的计算。尽管以前有很多关于这些非阿贝拉格柏特性的结果，包括对单个开放集合的导数的一些计算，