Categorical aspects in projective geometry
type: Item
instance of: scholarly article
title: Categorical aspects in projective geometry
zbMATH Open document ID: 0894.18004
DOI: 10.1023/A:1008632119843
author: C. Faure
author: Alfred Frölicher
published in: Applied Categorical Structures
publication date: 1998-09-07T00:00:00Z
review text: 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.
reviewed by: Philippe Elbaz-Vincent
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 51A05
Mathematics Subject Classification ID: 51A10
Mathematics Subject Classification ID: 18A20
zbMATH DE Number: 1138665
zbMATH Keywords: morphisms and homomorphisms of projective geometries
zbMATH Keywords: subgeometries
zbMATH Keywords: subspaces
zbMATH Keywords: quotient geometries
zbMATH Keywords: decomposition of morphism
zbMATH Keywords: factorization of morphisms
zbMATH Keywords: embeddings
MaRDI profile type: Publication
full work available at URL: a:1008632119843
OpenAlex ID: W1517043629
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description: scientific article; zbMATH DE number 1138665