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Initial and final completions

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References

  1. J.ADÁMEK, H.HERRLICH, G.E.STRECKER: Least and largest initial completions. Preprint.

    Google Scholar 

  2. -,-,-: The structure of initial completions. Preprint.

    Google Scholar 

  3. J. ADÁMEK, Y. KOUBEK: What to embed into a cartesion closed topological category. Comment.Math.Univ. Carolinae 18, 817–821 (1977).

    MathSciNet  MATH  Google Scholar 

  4. -.-: Cartesian closed fibre-completions. Preprint.

    Google Scholar 

  5. P. ANTOINE: Étude élémentaire des catégories d'ensembles structurés. Bull.Soc.Math.Belgique 18, 142–164 (1966).

    MathSciNet  MATH  Google Scholar 

  6. -: Extension minimale de la catégorie des espaces topologiques. C.R.Acad.Sc., Paris A 262, 1389–1392 (1966).

    MathSciNet  MATH  Google Scholar 

  7. B. BANASCHEWSKI, G. BRUNS: Categorical characterization of the Mac Neille completion. Archiv Math. 18, 369–377 (1967).

    Article  MathSciNet  MATH  Google Scholar 

  8. G.C.L. BROMMER, R.-E. HOFFMANN: An external characterization of topological functors. Springer Lecture Notes Math. 540, 136–151 (1976).

    Article  MathSciNet  Google Scholar 

  9. R.BÖRGER: Semitopologisch ≠ topologisch algebraisch. Preprint.

    Google Scholar 

  10. -: Universal topological completions of semi-topological functors over Ens need not exist. Preprint.

    Google Scholar 

  11. -: Legitimacy of certain topological completions. These Proceedings.

    Google Scholar 

  12. R.BÖRGER, W.THOLEN: Remarks on topologically algebraic functors Preprint.

    Google Scholar 

  13. G. Bourdaud: Some cartesian closed topological categories of convergence spaces. Springer Lecture Notes Math. 540, 93–108 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  14. N. BOURBAKI: Théorie des ensembles Ch.3 Ensembles ordonnés. Paris: Hermann 1963.

    MATH  Google Scholar 

  15. M. CHARTRELLE: Constructions de catégories auto-dominées. C.R.Acad. Sci., Paris A.B 274, 388–391 (1972).

    MathSciNet  MATH  Google Scholar 

  16. B. DAY: A reflection theorem for closed categories. J.pure appl. Algebra 2, 1–11 (1972).

    Article  MathSciNet  MATH  Google Scholar 

  17. H. HERRLICH: Cartesian closed topological categories. Math. Colloq. Univ. Cape Town 9, 1–16 (1974).

    MathSciNet  MATH  Google Scholar 

  18. -: Initial completions. Math.Z. 150, 101–110 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  19. -: Reflective Mac Neille completions of fibre-small categories need not be fibre-small. Comment.Math.Univ.Carolinae 19, 147–149 (1978).

    MathSciNet  MATH  Google Scholar 

  20. H.HERRLICH, R.NAKAGAWA, G.E.STRECKER, T.TITCOMB: Equivalence of semi-topological and topologically-algebraic functors. Canad.J.Math.

    Google Scholar 

  21. H. HERRLICH, L.D. NEL: Cartesian closed topological hulls. Proc. Amer. Math. Soc. 62, 215–222 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  22. H. HERRLICH, G.E. STRECKER: Category Theory. Allyn and Bacon, Boston 1973.

    MATH  Google Scholar 

  23. -,-: Semi-universal maps and universal initial completions. Pacific J.Math.

    Google Scholar 

  24. R.-E. HOFFMANN: Semi-identifying lifts and a generalization of the duality theorem for topological functors. Math. Nachr. 74, 295–307 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  25. -: Topological functors admitting generalized Cauchy-completions. Springer Lecture Notes Math. 540, 286–344 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  26. -: Topological completion of faithful functors. Kategorien-seminar 1, Hagen, 26–37 (1976).

    Google Scholar 

  27. -: Full reflective restrictions of topological functors. Math. Colloq. Univ. Cape Town 11, 65–88 (1977).

    MathSciNet  MATH  Google Scholar 

  28. -: Note on semi-topological functors. Math.Z. 160, 69–74 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  29. S.S. HONG: Categories in which every mono-source is initial. Kyungpook Math.J. 15, 133–139 (1975).

    MathSciNet  MATH  Google Scholar 

  30. Y.H.HONG: Studies on categories of universal topological algebras. Thesis, Mc Master Univ. 1974.

    Google Scholar 

  31. -: On initially structured functors. J.Korean Math.Soc. 14, 159–165 (1978).

    MathSciNet  MATH  Google Scholar 

  32. L. KUČERA, A. PULTR: On a mechanism of defining morphisms in concrete categories. Cahiers Topol. Géom. Diff. 13, 397–410 (1972).

    MathSciNet  MATH  Google Scholar 

  33. A. MACHADO: Espaces d'Antoine et pseudo-topologies, Cahiers Topol. Géom. Diff. 14, 309–327 (1973).

    MathSciNet  MATH  Google Scholar 

  34. E.G.MANES: Algebraic Theories, Springer Verlag 1975.

    Google Scholar 

  35. L.D. NEL: Initially structured categories and cartesian closedness. Canad.J.Math. 27, 1361–1377 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  36. -: Cartesian closed topological categories. Springer Lecture Notes Math. 540, 439–451 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  37. H.E. PORST: Characterization of Mac Neille completions and topological functors. Bull.Austral.Math.Soc. 18, 201–210 (1978).

    Article  MathSciNet  MATH  Google Scholar 

  38. Y.T. RHINEGHOST: Global completions. Preprint.

    Google Scholar 

  39. P.RINGLEB: Untersuchungen über die Kategorie der geordneten Mengen. Thesis, Free Univ. Berlin 1969.

    Google Scholar 

  40. E. SPANIER: Quasi-topologies. Duke Math.J. 30, 1–14 (1963).

    Article  MathSciNet  MATH  Google Scholar 

  41. W.THOLEN: Semi-topological functors. J.Pure Appl. Algebra

    Google Scholar 

  42. -: Konkrete Funktoren. Habilitationsschrift, Hagen 1978.

    Google Scholar 

  43. V. TRNKOVÁ: Automata and categories. Springer Lecture Notes Computer Sci. 32, 138–152 (1975).

    Article  MathSciNet  MATH  Google Scholar 

  44. M. WISCHNEWSKY: A lifting theorem for right adjoints. Cahiers Topol. Géom. Diff.

    Google Scholar 

  45. O. WYLER: Are there topoi in topology? Springer Lecture Notes Math. 540, 699–719 (1976).

    Article  MathSciNet  MATH  Google Scholar 

  46. R.-E. HOFFMANN: Note on universal topological completion. Preprint.

    Google Scholar 

  47. W. THOLEN: On Wyler's taut lifting theorem. Gen. Topol. Appl. 8, 197–206 (1978).

    Article  MathSciNet  MATH  Google Scholar 

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Horst Herrlich Gerhard Preuß

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© 1979 Springer-Verlag

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Herrlich, H. (1979). Initial and final completions. In: Herrlich, H., Preuß, G. (eds) Categorical Topology. Lecture Notes in Mathematics, vol 719. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065266

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  • DOI: https://doi.org/10.1007/BFb0065266

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  • Print ISBN: 978-3-540-09503-3

  • Online ISBN: 978-3-540-35193-1

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