We clarify in which precise sense the theory of principal bundles and the theory of groupoids are equivalent; and how this equivalence of theories, in the differentiable case, reflects itself in the theory of connections. The method used is that of synthetic differential geometry.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-8, author = {Anders Kock}, title = {Principal bundles, groupoids, and connections}, journal = {Banach Center Publications}, volume = {75}, year = {2007}, pages = {185-200}, zbl = {1121.51012}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-8} }
Anders Kock. Principal bundles, groupoids, and connections. Banach Center Publications, Tome 75 (2007) pp. 185-200. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-8/