Categories of projective geometries with morphisms and homomorphisms (Q1818582)

Projective geometries are introduced in the framework of Pasch geometries, as defined by \textit{D. K. Harrison} [Pac. J. Math. 80, 451-491 (1979; Zbl 0415.20022)], conditions on semi-linear maps to induce homomorphisms are provided, and several categories of projective geometries defined. A projective geometry is shown to be Desarguesian iff it is the homomorphic image of a higher-dimensional Desarguesian projective geometry.