Gauge transformations for categorical bundles

Abstract

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 and H 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 Λ H determine a categorical gauge transformation. More general gauge transformations are also studied.