Functorial scaling of ordinal data

In this paper we investigate how methods of deriving conceptual structures from ordinal data can be justified structurally. For the investigation we choose a categorical approach which is elaborated for suitable functors from the category of all ordinal structures to the category of all closure structures. The main result yields that the best functors are those which correspond to contra-ordinal scaling, a method developed in formal concept analysis (Formal Concept Analysis: Mathematical Foundations, Springer, Heidelberg, 1999).