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Categorical Aspects of Topology and Analysis pp 127–135Cite as

Universal completions of concrete categories

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Part of the book series: Lecture Notes in Mathematics ((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.

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References

  1. J. Adémek, H. Herrlich, G.E. Strecker, Least and largest initial competions. Comment. Math. Univ. Carolinae 20(1979), 43–77.

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  2. J. Adámek, V. Koubek, Completions of concrete categories. Preprint.

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  3. J. Adámek, V. Koubek, Cartesian closed concrete categories. Preprint.

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  4. Ch. Ehresmann, Prolongments universels d'un functeur par adjunction de limites. Dissertationes Math. 64 (1969).

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  5. H. Herrlich, Initial and final completions (Proc. Int. Conf. Cat. Top. Berlin 1978), Lecture Notes Math. 719 (1979) 137–149.

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  6. H. Herrlich, G.E. Strecker, Category Theory, 2 ed. Heldermann Verlag Berlin 1979.

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  7. J.R. Isbell, Small subcategories and completeness. Math. Syst. Theory 2 (1968), 27–50.

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  8. J. Lambek, Completions of categories, Lecture Notes Math. 24 (1966)

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  9. V. Trnková, Limits in categories and limit-preserving functors. Comment. Math. Univ. Carolinae 7 (1966) 1–73. *** DIRECT SUPPORT *** A00J4389 00005

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Authors
  1. Horst Herrlich
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B. Banaschewski

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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

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