Categorical aspects in projective geometry
After recalling an axiomatic definition of projective geometry and introducing morphisms between projective geometries, the authors study the category \(\mathcal P\)\textit{roj} of projective geometries and in particular the notions of embedding (i.e., initial monomorphism of \(\mathcal P\)\textit{roj}), quotient (i.e., final epimorphism of \(\mathcal P\)\textit{roj}) and factorization of morphisms. It is shown that there are three kinds of embeddings and two kinds of quotients. Furthermore the morphisms decompose in a canonical way into four factors. Several concrete examples are given.
morphisms and homomorphisms of projective geometries
scientific article; zbMATH DE number 1138665