The main goal for this paper is to revisit and rehabilitate structuralist methodology based on the idea of invariance and symmetry for the purpose of the discussion of structural realism and its consequences for ontology of information. This paper continues the earlier work of the author carried out in this spirit. In the present paper the focus is on the general concept of a structure, not necessarily in terms of information, but with important consequences for the study of structural information. The conceptual study of the general concept of a structure is followed by an outline of the mathematical formalism suitable for the development of its theory.