Scattering networks involve cascading wavelet transforms, modulus operators, and low-pass filtering. They provide a sound mathematical proxy to model and understand aspects of deep learning such as invariance, stability, hierarchical representation, role of nonlinear activation functions, etc. Linear translation-equivariant filtering based on convolution can be seen as a morphological erosion on a complete inf-semilattice defined by a specific partial ordering in the Fourier domain. In this case, ideal linear filters correspond to morphological openings. Using this framework, we provide a morphological interpretation of the scattering networks from the Fourier-based inf-semilattice. Then, we use the morphological universal representation theory to justify the universal representation of scattering networks of increasing operators on the Fourier-based inf-semilattice. Finally, using our theory we discuss the relevance of learning operators more general than wavelets in the frequency domain.