A categorical glimpse at the reconstruction of geometries

Abstract

The author's reconstruction method [‘Reconstruction of incidence geometries from groups of automorphisms’,Arch. Math. 58 (1992) 621–624] is put in a categorical setting, and generalized to geometries with an arbitrary number of ‘types’. The results amount to saying that the reconstruction process involves a pair of adjoint functors, and that the class of those geometries that are images under reconstruction forms a reflective subcategory.