Abstract
The notion of closure operator on a category is explored, utilizing the approach of Dikranjan and Giuli. Conditions on the underlying factorization structure are given, which allow the construction of closure operators satisfying a variety of extra conditions.
Keywords
- Closure Operator
- Separate Object
- Underlie Factorization Structure
- Composable Pair
- Grothendieck Topology
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References
J. Benabou and J. Roubaud, “Monades et descente,” C. R. Acad. Sc. Paris, t. 270, Série A (1970), 96–98.
J. Benabou, “Fibred categories and the foundations of naive category theory,” J. of Symbolic Logic50 (1985), 10–37.
R. Börger, Kategorielle Beschreibung von Zusammenhangsbegriffen, Thesis, Fernuniversität Hagen, Hagen, 1981.
G. Castellini, Closure Operators, Epimorphisms and Hausdorff Objects, Thesis, Kansas State University 1986.
G. Castellini, “Closure operators, monomorphisms and epimorphisms in categories of groups,” Cahiers Top. Geom. Diff. Cat.27, no. 2 (1986), 151–167.
D. Dikranjan and E. Giuli, “Closure operators I,” Topology and its Applications27, no. 2 (1987), 129–143.
J. Koslowski, Dedekind cuts and Frink ideals for categories, Thesis, Kansas State University 1986.
J. Koslowski, “CCCT-Hulls revisited,” to appear in Comm. Math. Univ. Carolinae.
R. Street, “The family approach to total cocompleteness and toposes,” Trans. Am. Math. Soc.284 (1984), 355–369.
W. Tholen, “Factorizations, localizations, and the orthogonal subcategory problem,” Math. Nachr. 114 (1983), 63–85.
W. Tholen, “Prereflections and Reflections,” Comm. in Algebra14 (1986), 717–740.
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© 1988 Springer-Verlag
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Koslowski, J. (1988). Closure operators with prescribed properties. In: Borceux, F. (eds) Categorical Algebra and its Applications. Lecture Notes in Mathematics, vol 1348. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0081360
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DOI: https://doi.org/10.1007/BFb0081360
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-50362-0
Online ISBN: 978-3-540-45985-9
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