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Martin Hofmann’s contributions to type theory: Groupoids and univalence

Published online by Cambridge University Press:  28 June 2021

Thorsten Altenkirch Open the ORCID record for Thorsten Altenkirch [Opens in a new window]
Thorsten Altenkirch*
Affiliation:
University of Nottingham, Nottingham NG7 2RD, UK Email: [email protected]
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Abstract

My goal is to give an accessible introduction to Martin’s work on the groupoid model and how it is related to the recent notion of univalence in Homotopy Type Theory while sharing some memories of Martin.

Keywords

Type TheoryGroupoidsUnivalence
Type
Paper
Information
Mathematical Structures in Computer Science , Volume 31 , Special Issue 9: In Homage to Martin Hofmann , October 2021 , pp. 953 - 957
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

Hofmann, M. and Streicher, T. (1998). The groupoid interpretation of type theory. In: Twenty-Five Years of Constructive Type Theory (Venice, 1995), vol. 36, 83–111.Google Scholar
Luo, Z. and Pollack, R. (1992). LEGO Proof Development System: User’s Manual . LFCS, Department of Computer Science, University of Edinburgh.Google Scholar
Martin-Löf, P. and Sambin, G. (1984). Intuitionistic Type Theory, vol. 9, Bibliopolis Naples.Google Scholar
Streicher, T. (2012). Semantics of Type Theory: Correctness, Completeness and Independence Results, Springer Science & Business Media, Berlin/Heidelberg, Germany.Google Scholar
The Univalent Foundations Program. Homotopy Type Theory: Univalent Foundations of Mathematics. https://homotopytypetheory.org/book, Institute for Advanced Study.Google Scholar
Vezzosi, A., Mörtberg, A. and Abel, A. (2019). Cubical agda: A dependently typed programming language with univalence and higher inductive types. Proceedings of the ACM on Programming Languages 3 (ICFP) 1–29.10.1145/3341691CrossRefGoogle Scholar