Gauge Transformations for Categorical Bundles

A gauge transformation of categorical principal bundles arises from a functorial isomorphism between such bundles. We determine the geometric nature of such gauge transformations. For a twisted-product categorical principal bundle whose structure group is given by a pair of Lie groups G andH we show that a pair consisting of a traditional gauge transformation θ, given by a G-valued function, and an L(H)-valued 1-form ΛH determine a categorical gauge transformation. More general gauge transformations are also studied.