Abstract
The topological universe hull of a concrete c-category over Set is compared with the cartesian closed topological and extensionable topological hulls. It is shown that the topological universe hull can be obtained from the other two hulls by a two-step process, in which the order of formation of hulls cannot be reversed. This provides also a correction of an existing description of the topological universe hull.
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References
Adámek, J., Classification of concrete categories, Houston J. Math. 12 (1986), 305–326.
Adámek, J. and H. Herrlich, Cartesian closed categories, quasitopoi and topological universes, Comment. Math. Univ. Carolinae 27 (1986), 235–257.
Adámek, J. and V. Koubek, Cartesian closed initial completions, Topology Appl. 11 (1980), 1–16.
Adámek, J. and J. Reiterman, The quasitopos hull of the category of uniform spaces, Topology Appl. 27 (1987), 97–104.
Adámek, J. and F. Schwarz, Description of the universally topological hull, in progress.
Bourdaud, G., Espaces d'Antoine et semi-espaces d'Antoine, Cahiers Top. Géom. Diff. 16 (1975), 107–133.
Gähler, W., Grundstrukturen der Analysis I, Akademie-Verlag, Berlin 1977.
Herrlich, H., Universal topology, in: H. L. Bentley et al. (eds.), Categorical Topology (Proc. Toledo 1983), Sigma Series Pure Math. 5, Heldermann, Berlin 1984, 223–281.
Herrlich, H., Topological improvements of categories of structured sets, Topology Appl. 27 (1987), 145–155.
Herrlich, H., Hereditary topological constructs, in: General Topology and its Relations to Modern Analysis and Algebra VI (Proc. Sixth Prague Topological Symposium 1986), Heldermann, Berlin 1988, 249–262.
Herrlich, H., On the representability of partial morphisms in Top and in related constructs, Proc. Summer Meeting on Category Theory, Louvain-la-Neuve 1987.
Herrlich, H. and L. D. Nel, Cartesian closed topological hulls, Proc. Amer. Math. Soc. 62 (1977), 215–222.
Marny, Th., On epireflective subcategories of topological categories, Gen. Topology Appl. 10 (1979), 175–181.
Nel, L. D., Topological universes and smooth Gelfand-Naimark duality, Contemporary Math. 30 (1984), 244–276.
Penon, J., Quasi-topos, C. R. Acad. Sc. Paris, Sér. A, 276 (1973), 237–240.
Penon, J., Sur les quasi-topos, Cahiers Topol. Géom. Diff. 18 (1977), 181–218.
Schwarz, F., Hereditary topological categories and topological universes, Quaest. Math. 10 (1986), 197–216.
Schwarz, F., Heredity in topological and monotopological categories, Preprint 1986.
Wyler, O., Are there topoi in topology?, in: E. Binz et al. (eds.), Categorical Topology (Proc. Mannheim 1975), Lecture Notes Math. 540, Springer, Berlin — Heidelberg — New York 1976, 699–719.
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© 1989 Springer-Verlag Berlin Heidelberg
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Schwarz, F. (1989). Description of the topological universe hull. In: Ehrig, H., Herrlich, H., Kreowski, H.J., Preuß, G. (eds) Categorical Methods in Computer Science With Aspects from Topology. Lecture Notes in Computer Science, vol 393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51722-7_21
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DOI: https://doi.org/10.1007/3-540-51722-7_21
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