Hypergraphs can be built from a formal context, and conversely formal contexts can be derived from a hypergraph. Establishing such links allows exploiting morphological operators developed in one framework to derive new operators in the other one. As an example, the combination of derivation operators on formal concepts leads to closing operators on hypergraphs which are not the composition of dilations and erosions. Several other examples are investigated in this paper, with the aim of processing formal contexts and hypergraphs, and navigating in such structures.