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Regularity of the category of Kelley spaces

Abstract

We show that the cartesian closed category of compactly generated Hausdorff spaces is regular, but is neither exact, nor locally cartesian closed. In fact we find a coequalizer of an equivalence relation which is not stable under pullback.

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Cagliari, F., Mantovani, S. & Vitale, E.M. Regularity of the category of Kelley spaces. Appl Categor Struct 3, 357–361 (1995). https://doi.org/10.1007/BF00872904

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Mathematics Subject Classifications (1991)

  • 18B30
  • 54D50
  • 18D15

Key words

  • compactly generated spaces
  • regular and exact categories
  • locally cartesian closed categories