Modern Projective Geometry pp 127-155 | Cite as

# Morphisms of Projective Geometries

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## Abstract

Since a morphism from a projective geometry *G* _{1} to another one *G* _{2} is a map that is defined on certain, but in general not on all points of *G* _{1}, we begin the chapter with some generalities on the so-called partial maps. A partial map from a set *X* to a set *Y*, noted *f: X* - -→ *Y*,is a map *f* from a subset of *X*, called the *domain* of *f*,to Y. The points of *X* which are not in the domain of *f* form the so-called *kernel* of *f.* The sets together with the partial maps form a category **Par**. In the first section we give some elementary basic facts concerning this category. One can avoid partial maps by working with the equivalent category **Set*** of pointed sets. This is sometimes quite useful, but it involves that one has to add to the points of every projective geometry an additional point which can be considered as the zero element of the lattice of subspaces, but has no direct geometric interpretation.

## Keywords

Vector Space Irreducible Component Projective Geometry Canonical Projection Vector Subspace## Preview

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