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Universal completions of concrete categories

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Part of the Lecture Notes in Mathematics book series (LNM,volume 915)

Abstract

For every concerete category (A,U) over a complete base category X, Ch. Ehresmann has constructed a concrete completion. The objects of his completion are obtained by a transfinite process. J Adámek and V. Koubek have been able to obtain the objects of such a completion in one step, but still need a transfinite process to obtain the morphisms. In this paper a one-step-construction for such a completion is provided. The latter two completions are characterized by the obvious universal property, hence equivalent. The first completion is different.

Keywords

  • Small Category
  • Unique Extension
  • Complete Category
  • Canonical Embedding
  • Structure Source

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References

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© 1982 Springer-Verlag

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Herrlich, H. (1982). Universal completions of concrete categories. In: Banaschewski, B. (eds) Categorical Aspects of Topology and Analysis. Lecture Notes in Mathematics, vol 915. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0092876

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  • DOI: https://doi.org/10.1007/BFb0092876

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11211-2

  • Online ISBN: 978-3-540-39041-1

  • eBook Packages: Springer Book Archive