Schematizing territories using Q-analysis and category theory

Territories are usually designed, structured and represented in reference to the physical space. Yet the geographical dimension and in particular the distribution of populations and cities in the territories has already demonstrated that it could not be reduced to this single affine and homogeneous space. The dematerialization of information material accelerates and makes visible this structural gap between physical space and territories. The mathematical tools built around the mathematization of geometry are used to analyze the difference. This is the case of Q-analysis, but also of the theory of categories. Q-analysis has already been used to analyse various situations in the humanities.
We will present this tool (Q-analysis) and show how it operated in the humanities and in particular to study territories.
Regarding the theory of categories, the connective space concepts or point without spaces allow a fresh look on the territories. We will present the concepts of category theory from which are derived the methods of Q-analysis. We will explain the concepts of connective space or space without points that allow a fresh look on the territories.