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Homotopy-Theoretic Models of Type Theory

  • Peter Arndt
  • Krzysztof Kapulkin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6690)

Abstract

We introduce the notion of a logical model category, which is a Quillen model category satisfying some additional conditions. Those conditions provide enough expressive power that one can soundly interpret dependent products and sums in it while also having a purely intensional interpretation of the identity types. On the other hand, those conditions are easy to check and provide a wide class of models that are examined in the paper.

Keywords

Model Category Type Theory Weak Equivalence Grothendieck Topology Weak Factorization System 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Peter Arndt
    • 1
  • Krzysztof Kapulkin
    • 2
  1. 1.University of OsloOsloNorway
  2. 2.University of PittsburghPittsburghUSA

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