Hostname: page-component-758b78586c-qvhcc Total loading time: 0 Render date: 2023-11-30T01:37:43.266Z Has data issue: false Feature Flags: { "corePageComponentGetUserInfoFromSharedSession": true, "coreDisableEcommerce": false, "useRatesEcommerce": true } hasContentIssue false

A dependently-typed construction of semi-simplicial types

Published online by Cambridge University Press:  20 November 2014

HUGO HERBELIN*
Affiliation:
INRIA, PPS, Université Paris-Diderot, Case 7014, 75205 Paris Cedex 13, France Email: Hugo.Herbelin@inria.fr
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not possible as this article does not have html content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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).

Type
Paper
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) 353423.Google 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.Google 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
Supplementary material: File

Herbelin supplementary material

Supplementary material

Download Herbelin supplementary material(File)
File 48 KB