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Mathematical Structures in Computer Science Mathematical Structures in Computer Science

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A dependently-typed construction of semi-simplicial types

Published online by Cambridge University Press:  20 November 2014

HUGO HERBELIN
HUGO HERBELIN*
Affiliation:
INRIA, PPS, Université Paris-Diderot, Case 7014, 75205 Paris Cedex 13, France Email: Hugo.Herbelin@inria.fr
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Abstract

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This paper presents a dependently-typed construction of semi-simplicial sets in a type theory where sets are taken to be types. This addresses an open question raised on the wiki of the special year on Univalent Foundations at the Institute of Advanced Study (2012–2013).

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Mathematical Structures in Computer Science , Volume 25 , Special Issue 5: From type theory and homotopy theory to Univalent Foundations of Mathematics , June 2015 , pp. 1116 - 1131
Copyright
Copyright © Cambridge University Press 2014 

References

Coq Development Team, T. (2012) The Coq Reference Manual, version 8.4. Available at http://coq.inria.fr/doc.Google Scholar
Friedman, G. (2012) Survey article: An elementary illustrated introduction to simplicial sets. Rocky Mountain Journal of Mathematics 42 (2) 353–423.CrossRefGoogle Scholar
LeFanu Lumsdaine, P. (2012) Semi-simplicial types. Available at: http://uf-ias-2012.wikispaces.com/Semi-simplicial+types.Google Scholar
The Univalent Foundations Program, Institute of Advanced Study. (2013) Homotopy Type theory: Univalent Foundations of Mathematics. Available at http://homotopytypetheory.org/book.Google Scholar
Voevodsky, V. (2011) Univalent foundations of mathematics. In: Logic, Language, Information and Computation. Springer Lecture Notes in Computer Science 6642, Berlin-Heidelberg 4.CrossRefGoogle Scholar
Voevodsky, V. (2012a) Semi-simplicial types. Available at http://uf-ias-2012.wikispaces.com/Semi-simplicial+types.Google Scholar
Voevodsky, V. (2012b) Univalent foundations repository. Ongoing Coq development. Available at https://github.com/vladimirias/Foundations.Google Scholar
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