An article that we are preparing
For the moment, an exposition of some aspects can be found in
WZW terms in a cohesive -topos ,
talk at Representation Theoretic and Categorical Structures in Quantum Geometry and Conformal Field Theory (2011)
In the context of differential cohomology in a cohesive topos, every characteristic map induces – via ∞-Chern-Weil theory – the Lagrangian of an ∞-Chern-Simons theory. There is canonically a differentially twisted looking of . This generalizes the Lagrangian for the sigma-model called the Wess-Zumino-Witten model from Lie group target spaces to general smooth ∞-group target spaces.