Structure in cognitive developmental research: An approach from a mathematical category theory

Abstract

One important problem in current cognitive development research is the lack of theory. In this article, therefore, we propose a cognitive development theory based on mathematical structures. Specifically, we first focus on the concept of structure, which is the concept Piaget introduced to cognitive developmental research. Piaget’s theory was mainly inspired by mathematical group and lattice, but many concepts Piaget himself invented (e.g., grouping) were difficult to deal with in a mathematically rigorous manner. Therefore, here, the authors recapture some of the concepts proposed by Piaget in a mathematically understandable form based on the concept of mathematical category, a generalization of the group. Furthermore, we would like to introduce cognitive developmental research on structural concepts since Piaget and suggest directions for future research.