Univalence for inverse diagrams and homotopy canonicity

@article{Shulman2015UnivalenceFI,
  title={Univalence for inverse diagrams and homotopy canonicity},
  author={Michael Shulman},
  journal={Mathematical Structures in Computer Science},
  year={2015},
  volume={25},
  pages={1203-1277}
}
We describe a homotopical version of the relational and gluing models of type theory, and generalize it to inverse diagrams and oplax limits. Our method uses the Reedy homotopy theory on inverse diagrams, and relies on the fact that Reedy fibrant diagrams correspond to contexts of a certain shape in type theory. This has two main applications. First, by considering inverse diagrams in Voevodsky’s univalent model in simplicial sets, we obtain new models of univalence in a number of (∞, 1… CONTINUE READING
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References

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Showing 1-10 of 25 references

The simplicial model of univalent

  • C. 179–208. Kapulkin, P. L. Lumsdaine, V. Voevodsky
  • 2012
Highly Influential
20 Excerpts

Univalence in locally Cartesian closed 1-categories. ArXiv:1208.1749

  • D. Gepner, J. Kock
  • Journal of Functional
  • 2012
Highly Influential
6 Excerpts

On the interpretation of type theory in locally cartesian closed categories

  • M. Hofmann
  • 1994
Highly Influential
6 Excerpts

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