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The category of points of a projective space. (Catégorie des points d’un espace projectif.) (French) Zbl 0797.51004

Summary: We describe a category introduced by A. Kock [‘The category aspect of projective space’, Aarhus Univ., preprint Nr. 7 (1974)] whose objects are the points of a projective space, and whose morphisms between two distinct points \(P\) and \(Q\) are the other points of the line \((PQ)\). Then we give categorical proofs of theorems of projective geometry.

MSC:

51A05 General theory of linear incidence geometry and projective geometries
18F99 Categories in geometry and topology
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References:

[1] S. Mac Lane , Categories for the working mathematician , Springer-Verlag , 1972 . MR 354798 | Zbl 0232.18001 · Zbl 0232.18001
[2] A. Kock , The category aspect of projective space , Aarhus Universitet preprint n^\circ 7 , 1974 .
[3] M. Berger , Géométrie , vol. tome 1, Cedic Nathan , 1977 .
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