Application of prismatic constructions to gauge field theory (Q428825)

Prismatic sets where introduced in [\textit{J. L. Dupont} and \textit{R. Ljungmann}, Math. Scand. 97, No. 1, 11--39 (2005; Zbl 1101.14024)] in order to have a construction of an integration map in smooth Deligne theory. The author gives a connection in a bundle over the prismatic subdivision of a simplicial set \(S\) using the classifying map. Also the author provides the evaluation of the Chern-Simons form for the prismatic subdivision and the variational formula for the Chern-Simons classes of a given bundle with a connection.