Abstract
For a concrete, topological category K over a suitable base category, the interrelationship of the concepts in the title is investigated. K is cartesian closed iff regular sinks are finitely productive. K is a quasitopos iff regular sinks are universal. For categories over Set with constant maps, the latter are precisely the topological universes. These can also be described as categories of sieves for Grothendieck topologies.
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© 1986 Springer-Verlag Berlin Heidelberg
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Adámek, J., Herrlich, H. (1986). Cartesian closed categories, quasitopoi and topological universes. In: Melton, A. (eds) Mathematical Foundations of Programming Semantics. MFPS 1985. Lecture Notes in Computer Science, vol 239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-16816-8_23
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DOI: https://doi.org/10.1007/3-540-16816-8_23
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