We construct and establish results for a categorical counterpart of pushforwards of connections on principal bundles. This categorical pushforward takes as input a categorical connection A_P on a categorical bundle P and an appropriate functor S: P -> Q and outputs a categorical connection S_*A_P on the categorical bundle Q. Applying this construction to the case of categorical bundles arising from decorated path spaces in principal bundles, we obtain a transformation of classical connections that combines the traditional gauge transformation with an affine translation.
Keywords: Categorical Groups; Categorical geometry; Principal bundles; Gauge Theory
2020 MSC: Primary: 18D05; Secondary: 20C99
Theory and Applications of Categories, Vol. 38, 2022, No. 25, pp 1015-1049.