Non-Constructivity in Kan Simplicial Sets

  title={Non-Constructivity in Kan Simplicial Sets},
  author={M. Bezem and T. Coquand and Erik Parmann},
We give an analysis of the non-constructivity of the following basic result: if X and Y are simplicial sets and Y has the Kan extension property, then Y^X also has the Kan extension property. By means of Kripke countermodels we show that even simple consequences of this basic result, such as edge reversal and edge composition, are not constructively provable. We also show that our unprovability argument will have to be refined if one strengthens the usual formulation of the Kan extension… Expand

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