Applied Categorical Structures

, Volume 9, Issue 5, pp 497–504 | Cite as

Realizations of Topological Categories

  • R. Rother


There are functor-preordering-structured categories S(F,P), defined by the Prague School, in which every concrete category over a concretizable basecategory is realizable. Over nice basecategories there are realizations of all topological categories in some topological S(F,L). This gives rise for a new characterization of those concrete categories having a topological hull.

initial completion concrete universal category topologically universal category universal complete lattice 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Adámek, J., Herrlich, H. and Strecker, G. E.: Least and largest initial completions-I, II, Comment. Math. Univ. Carolin. 20 (1) (1979), 43-77.Google Scholar
  2. 2.
    Adámek, J., Herrlich, H. and Strecker, G. E.: Abstract and Concrete Categories, Wiley, New York, 1990.Google Scholar
  3. 3.
    Gillman, L. and Jerison, M.: Rings of Continuous Functions, Van Nostrand, Princeton, 1960.Google Scholar
  4. 4.
    Hedrlín, Z.: On universal partly ordered sets and classes, J. Algebra 11 (1969), 503-509.Google Scholar
  5. 5.
    Herrlich, H.: Initial Completions, Math. Z. 150 (1976), 101-110.Google Scholar
  6. 6.
    Kučera, L.: Lectures from the theory of categories (Czech), Preprint, Charles Univ., 1970.Google Scholar
  7. 7.
    Kučera, L.: On universal concrete categories, Algebra Universalis 5 (1975), 149-151.Google Scholar
  8. 8.
    Kučera, L. and Pultr, A.: On a mechanism of defining morphisms in concrete categories, Cahiers Topologie Géom. Différentielle Catégoriques 13 (1972), 397-410.Google Scholar
  9. 9.
    Pultr, A. and Trnková, V.: Combinatorial, Algebraic and Topological Representations of Groups, Semigroups and Categories, North-Holland, Amsterdam, 1980.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • R. Rother
    • 1
  1. 1.University of BremenGermany

Personalised recommendations