A categorical principal bundle is a structure comprised of categories that is analogous to a classical principal bundle; examples arise from geometric contexts involving bundles over path spaces. We show how a categorical principal bundle can be constructed from local data specified through transition functors and natural transformations.
Keywords: Categorical Groups; 2-Groups; Categorical geometry; Principal bundles
2010 MSC: Primary: 18D05; Secondary: 20C99
Theory and Applications of Categories, Vol. 31, 2016, No. 14, pp 388-417.