From the advent of general purpose, Turing-complete machines, the relation between operators, programmers and users with computers can be observed as interconnected informational organisms (inforgs), henceforth analysed with the method of levels of abstraction (LoAs), risen within the philosophy of information (PI). In this paper, the epistemological levellism proposed by L. Floridi in the PI to deal with LoAs will be formalised in constructive terms using category theory, so that information itself is treated as structure-preserving functions instead of Cartesian products. The milestones in the history of modern computing are then analysed through constructive levellism to show how the growth of system complexity lead to more and more information hiding.