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Kan extensions in effective semantics

  • Philip S. Mulry
Part I Categorical And Algebraic Methods
Part of the Lecture Notes in Computer Science book series (LNCS, volume 298)

Abstract

An extension property for maps between domains is generalized to a categorical setting where the notions of adjoint and Kan extension are utilized to prove an extension property for functors. The results are used in an effective setting to provide a new characterization for certain computable mappings.

Keywords

Natural Transformation Extension Property Effective Operation Continuous Lattice Left Adjoint 
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. [E]
    Ersov, Ju. Model C of Partial Continuous Functions, in Logic Colloquium 76. Amsterdam: North Holland, 1977.Google Scholar
  2. [J]
    Johnstone, P. T. Stone Spaces. Cambridge: Cambridge University Press, 1982.Google Scholar
  3. [ML]
    MacLane, S. Categories for the Working Mathematician. New York: Springer-Verlag, 1971.Google Scholar
  4. [M1]
    Mulry, P. S. Generalized Banach-Mazur Functionals in the Topos of Recursive Sets, Journal of Pure and Applied Algebra, 26 (1982), 71–83.CrossRefGoogle Scholar
  5. [M2]
    Mulry, P. S. Adjointness in Recursion, Annals of Pure and Applied Logic, 32 (1986).Google Scholar
  6. [M3]
    Mulry, P. S. A Categorical Approach to the Theory of Computation. Preprint, 1986.Google Scholar
  7. [R]
    Rogers, H. Theory of Recursive Functions and Effective Computability. New York: McGraw-Hill, 1967.Google Scholar
  8. [S1]
    Scott, D. Continuous Lattices, in Toposes, Algebraic Geometry and Logic. New York: Springer-Verlag, 1972.Google Scholar
  9. [S2]
    Scott, D. Lectures on a Mathematical Theory of Computation. Technical Monograph PRG-19. Oxford University, 1981.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Philip S. Mulry
    • 1
  1. 1.Colgate UniversityHamilton

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