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Completeness and cocompleteness of the categories of basic pairs and concrete spaces

  • HAJIME ISHIHARA (a1) and TATSUJI KAWAI (a1)
Abstract

We show that the category of basic pairs (BP) and the category of concrete spaces (CSpa) are both small-complete and small-cocomplete in the framework of constructive Zermelo–Frankel set theory extended with the set generation axiom. We also show that CSpa is a coreflective subcategory of BP.

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P. Aczel (1978) The type theoretic interpretation of constructive set theory. In: A. MacIntyre , L. Pacholski and J. Paris (eds.) Logic Colloquium '77, North Holland, Amsterdam 5566.

P. Aczel (1982) The type theoretic interpretation of constructive set theory: Choice principles. In: A. S. Troelstra and D. van Dalen (eds.) The L.E.J. Brouwer Centenary Symposium, North Holland, Amsterdam 140.

P. Aczel (2006) Aspects of general topology in constructive set theory. Annals of Pure and Applied Logic 137 (13) 329.

A. Bucalo and G. Rosolini (2006) Completions, comonoids, and topological spaces. Annals of Pure and Applied Logic 137 (13) 104125.

T. Coquand , G. Sambin , J. Smith and S. Valentini (2003) Inductively generated formal topologies. Annals of Pure and Applied Logic 124 (13) 71106.

H. Ishihara and E. Palmgren (2006) Quotient topologies in constructive set theory and type theory. Annals of Pure and Applied Logic 141 (12) 257265.

H. Ishihara and P. Schuster (2004) Compactness under constructive scrutiny. Mathematical Logic Quarterly 50 (6) 540550.

G. Sambin (1987) Intuitionistic formal spaces – a first communication. In: D. Skordev (ed.) Mathematical Logic and its Applications, volume 305, Plenum Press 187204.

G. Sambin and S. Gebellato (1999) A preview of the basic picture: A new perspective on formal topology. In: T. Altenkirch , B. Reus and W. Naraschewski (eds.) Types for Proofs and Programs. Springer Lecture Notes in Computer Science 1657 194208.

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Mathematical Structures in Computer Science
  • ISSN: 0960-1295
  • EISSN: 1469-8072
  • URL: /core/journals/mathematical-structures-in-computer-science
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