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Books Year : 2013

Homotopy Type Theory: Univalent Foundations of Mathematics

1 University of Manchester [Manchester]
2 IRIT-ACADIE - Assistance à la Certification d’Applications DIstribuées et Embarquées
3 Functional Programming Laboratory
4 CMU - Carnegie Mellon University [Pittsburgh]
5 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
6 University of Ljubljana
7 MARELLE - Mathematical, Reasoning and Software
8 IAS - Institute for Advanced Study [Princeton]
9 CSE - Department of Computer Science and Engineering [Göteborg]
10 NSF - National Science Foundation [Arlington]
11 PI.R2 - Design, study and implementation of languages for proofs and programs
12 PPS - Preuves, Programmes et Systèmes
13 Stockholm University
14 SPECFUN - Symbolic Special Functions : Fast and Certified
15 IHPST - Institute for the History and Philosophy of Science and Technology
16 RFBR - Russian Foundation for Basic Research
17 WUSTL - Washington University in Saint Louis
18 SDSU - San Diego State University
19 ICIS - Institute for Computing and Information Sciences [Nijmegen]
20 ILLC - Institute for Logic, Language and Computation
21 CU - Charles University [Prague]
22 LJAD - Laboratoire Jean Alexandre Dieudonné
23 UWO - University of Western Ontario
24 Cornell University [New York]
25 University of Birmingham [Birmingham]
26 School of Mathematics [Leeds]
27 DPMMS - Department of Pure Mathematics and Mathematical Statistics
28 MSR - INRIA - Microsoft Research - Inria Joint Centre
29 LMU - Institut für Informatik [München/Munich]
30 Department of Mathematics and Statistics [Ottawa]
31 JGU - Johannes Gutenberg - Universität Mainz = Johannes Gutenberg University
32 UON - University of Nottingham, UK
33 BCM - Baylor College of Medicine
34 Royal Holloway University of London - Department of Computer Science
35 Department of Mathematics Stockholm University
36 Princeton University
Yves Bertot
Dana Scott
  • Function : Author


Homotopy type theory is a new branch of mathematics that combines aspects of several different fields in a surprising way. It is based on a recently discovered connection between homotopy the- ory and type theory. Homotopy theory is an outgrowth of algebraic topology and homological algebra, with relationships to higher category theory; while type theory is a branch of mathematical logic and theoretical computer science. Although the connections between the two are currently the focus of intense investigation, it is increasingly clear that they are just the beginning of a subject that will take more time and more hard work to fully understand. It touches on topics as seemingly distant as the homotopy groups of spheres, the algorithms for type checking, and the definition of weak ∞-groupoids.
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Dates and versions

hal-00935057 , version 1 (23-01-2014)


  • HAL Id : hal-00935057 , version 1


Peter Aczel, Benedikt Ahrens, Thorsten Altenkirch, Steve Awodey, Bruno Barras, et al.. Homotopy Type Theory: Univalent Foundations of Mathematics. Aucun, pp.448, 2013. ⟨hal-00935057⟩
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