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.
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