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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


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]).


Topological Space Number Theory Algebraic Geometry Topological Group Space Object 
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    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
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    DIACONESCU, RADU: Change of Base for Some Toposes, Thesis, Dalhousie 1973.Google Scholar
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    KOCK, ANDERS and WRAITH, GAVIN: Elementary Toposes, Lecture Notes Series 30, Aarhus Universitat Matematisk Institut 1970.Google Scholar
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    LAWVERE, F. WILLIAM: Quantifiers and Sheaves, Actes du Congrès Int. des Math. Nice 1970, I, 329–334.Google Scholar
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    OSIUS, GERHARD: Categorical Set Theory: a Characterization of the Category of Sets, J. Pure and Appl.Alg. Vol.4, 79–120 (1974).Google Scholar
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    OSIUS, GERHARD: The Internal and External Aspect of Logic and Set Theory in Elementary Topoi, preprint, 1974.Google Scholar
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    STOUT, LAWRENCE: General Topology in an Elementary Topos, Thesis, University of Illinois, 1974.Google Scholar
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    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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