  The c-map of four dimensional non-linear theories of electromagnetism is
considered both in the rigid case and in its coupling to gravity. In this way
theories with antisymmetric tensors and scalars are obtained, and the three
non-linear representations of N=2 supersymmetry partially broken to N=1
related. The manifest $\mathrm{Sp}(2n)$ and $\mathrm{U}(n)$ covariance of these
theories in their multifield extensions is also exhibited.
