Abstract
Geometries over a typeset I are defined in terms of multipartite graphs, enabling the language of graphs to describe flags and their residues, truncations, and shadows. Similarly, morphisms of geometries are type-preserving graph morphisms. Truncation is then seen as a functor between categories of geometries. The relation of morphism and residues is more tenuous. The chapter concludes with a discussion of residual connectedness, and exercises.
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References
Francis Buekenhout. The basic diagram of a geometry. In Martin Aigner and Dieter Jungnickel, editors, Geometries and Groups, pages 1–29. Springer, Berlin, 1981.
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© 2011 Springer-Verlag Berlin Heidelberg
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Shult, E.E. (2011). Geometries: Basic Concepts. In: Points and Lines. Universitext. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15627-4_2
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DOI: https://doi.org/10.1007/978-3-642-15627-4_2
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15626-7
Online ISBN: 978-3-642-15627-4
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