Group-Theoretic Axioms For Projective Geometry

Abstract

AbstractWe show that a certain category 𝓖 whose objects are pairs G ⊃ H of groups subject to simple axioms is equivalent to the category of ≧ 2-dimensional vector spaces and injective semi-linear maps; and deduce via the "Fundamental Theorem of Projective Geometry" that the category of ≧ 2-dimensional projective spaces is equivalent to the quotient of a suitable subcategory of 𝓖 by the least equivalence relation which identifies conjugation by any element of H with the identity automorphism of G.