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Intersections of reflective subcategories


Authors: J. Adámek and J. Rosický
Journal: Proc. Amer. Math. Soc. 103 (1988), 710-712
MSC: Primary 18A40; Secondary 18B30, 54B30
DOI: https://doi.org/10.1090/S0002-9939-1988-0947643-9
MathSciNet review: 947643
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Abstract: It is shown that the class of full reflective subcategories of $ \mathcal{Fq}$ (and of other concrete categories) is not closed under intersections. This answers a question raised by Herrlich in 1967. A natural example of nonreflective intersection is presented in the category of bitopological spaces.


References [Enhancements On Off] (What's this?)

  • [A] J. Adámek, Theory of mathematical structures, Reidel, Dordrecht, 1983.
  • [H1] H. Herrlich, Topologische Reflexionen und Coreflexionen, Lecture Notes in Math., vol. 78, Springer-Verlag, Berlin and New York, 1968. MR 0256332 (41:988)
  • [H2] -, Topological functors, General Topology Appl. 4 (1974), 125-142. MR 0343226 (49:7970)
  • [HS] H. Herrlich and G. E. Strecker, Category theory, Allyn and Bacon, Boston, Mass., 1973. MR 0349791 (50:2284)
  • [Ke] M. Kelly, A unified treatment of transfinite constructions for free algebras, free monoids, cotimits, associated aheaves, and so on, Bull. Austral. Math. Soc. 22 (1980), 1-84. MR 589937 (82h:18003)
  • [Ko] V. Koubek, Each concrete category has a representation by $ {T_2}$ paracompact topological spaces, Comment. Math. Univ. Carolinae 15 (1975), 655-664. MR 0354806 (50:7283)
  • [PT] A. Pultr and V. Trnková, Combinatorial, algebraic and topological representations of groups, semigroups and categories, North-Holland, Amsterdam, 1980. MR 563525 (81d:18001)
  • [T] W. Tholen, Reflective subcategories. I, Proc. Conf. Categorical Topology (L'Aquila 1986), Topology and Appl. (to appear) MR 911692 (89b:18006)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0947643-9
Article copyright: © Copyright 1988 American Mathematical Society

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