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, Volume 17, Issue 1, pp 1–14 | Cite as

Topological space objects in a topos II: ɛ-Completeness and ɛ-cocompleteness

  • Lawrence Neff Stout
Article

Abstract

It is well known that topoi satisfy strong internal completeness and cocompleteness conditions: Lawvere [4] announced the existence of internal Kan extensions; proofs may be found in Kock and Wraith [3] and Diaconescu [2]. In this paper I give an explicit construction of the limit of an internal functor and lift the completeness and cocompleteness of ɛ to the category of topological space objects in ɛ defined by internalizing the definition in terms of open sets (as in [7] and [8]).

Keywords

Topological Space Number Theory Algebraic Geometry Topological Group Space Object 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    BENABOU, JEAN: Introduction to Bicategories, in Reports of the Midwest Category Theory Seminar, Lecture Notes in Mathematics 47. Berlin, Heidelberg, and New York: Springer 1967.Google Scholar
  2. [2]
    DIACONESCU, RADU: Change of Base for Some Toposes, Thesis, Dalhousie 1973.Google Scholar
  3. [3]
    KOCK, ANDERS and WRAITH, GAVIN: Elementary Toposes, Lecture Notes Series 30, Aarhus Universitat Matematisk Institut 1970.Google Scholar
  4. [4]
    LAWVERE, F. WILLIAM: Quantifiers and Sheaves, Actes du Congrès Int. des Math. Nice 1970, I, 329–334.Google Scholar
  5. [5]
    OSIUS, GERHARD: Categorical Set Theory: a Characterization of the Category of Sets, J. Pure and Appl.Alg. Vol.4, 79–120 (1974).Google Scholar
  6. [6]
    OSIUS, GERHARD: The Internal and External Aspect of Logic and Set Theory in Elementary Topoi, preprint, 1974.Google Scholar
  7. [7]
    STOUT, LAWRENCE: General Topology in an Elementary Topos, Thesis, University of Illinois, 1974.Google Scholar
  8. [8]
    STOUT, LAWRENCE: Topological Space Objects in a Topos I: Variable Spaces for Variable Sets. To appear.Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • Lawrence Neff Stout
    • 1
  1. 1.Department of MathematicsMcGill UniversityMontréalCanada

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