Path Spaces of Higher Inductive Types in Homotopy Type Theory

@article{Kraus2019PathSO,
  title={Path Spaces of Higher Inductive Types in Homotopy Type Theory},
  author={N. Kraus and J. V. Raumer},
  journal={2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  year={2019},
  pages={1-13}
}
  • N. Kraus, J. V. Raumer
  • Published 2019
  • Mathematics, Computer Science
  • 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
  • The study of equality types is central to homotopy type theory. Characterizing these types is often tricky, and various strategies, such as the encode-decode method, have been developed. We prove a theorem about equality types of coequalizers and pushouts, reminiscent of an induction principle and without any restrictions on the truncation levels. This result makes it possible to reason directly about certain equality types and to streamline existing proofs by eliminating the necessity of… CONTINUE READING
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    References

    SHOWING 1-10 OF 56 REFERENCES
    Higher Inductive Types as Homotopy-Initial Algebras
    • 38
    • Highly Influential
    • PDF
    Univalent higher categories via complete Semi-Segal types
    • 14
    • PDF
    The real projective spaces in homotopy type theory
    • Ulrik Buchholtz, E. Rijke
    • Mathematics, Computer Science
    • 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
    • 2017
    • 10
    • PDF
    Calculating the Fundamental Group of the Circle in Homotopy Type Theory
    • 67
    • Highly Influential
    • PDF
    Eilenberg-MacLane spaces in homotopy type theory
    • 40
    • PDF
    The Integers as a Higher Inductive Type
    • 5
    • Highly Influential
    • PDF
    Higher Groups in Homotopy Type Theory
    • 13
    • PDF
    Free Higher Groups in Homotopy Type Theory
    • 7
    • PDF
    Homotopy Type Theory: Univalent Foundations of Mathematics
    • 54
    • PDF