Die Kategorie der Kettengeometrien. (The category of chain geometries) (Q1099405)

In order to provide a convenient setting for the theory of chain geometries the category of curve spaces (German: Kurvenräume) is introduced. The mappings which assign to a finite dimensional K-algebra its associated projective or affine chain geometry turn out to be functors from the category of finite dimensional K-algebras to the category of curve spaces. These functors respect finite products. Also discussed are chain geometries which are associated with modules over finite dimensional K-algebras and their behaviour with respect to the category of curve spaces.