Univalent foundations (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Univalent foundations" in English language version.

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8arxiv.org

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2ias.edu

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ams.org

Pelayo, Álvaro; Warren, Michael A. (2014). "Homotopy type theory and Voevodsky's univalent foundations". Bulletin of the American Mathematical Society. 51 (4): 597–648. arXiv:1210.5658. doi:10.1090/S0273-0979-2014-01456-9.
Grayson, Daniel R. (2018). "An introduction to univalent foundations for mathematicians". Bulletin of the American Mathematical Society. 55 (4): 427–450. arXiv:1711.01477. doi:10.1090/bull/1616. S2CID 32293255.

arxiv.org

Martín Hötzel Escardó (October 18, 2018) A self-contained, brief and complete formulation of Voevodsky’s Univalence Axiom
See Ahrens, Benedikt; Kapulkin, Chris; Shulman, Michael (2015). "Univalent categories and the Rezk completion". Mathematical Structures in Computer Science. 25 (5): 1010–1039. arXiv:1303.0584. doi:10.1017/S0960129514000486. S2CID 1135785.
Pelayo, Álvaro; Warren, Michael A. (2014). "Homotopy type theory and Voevodsky's univalent foundations". Bulletin of the American Mathematical Society. 51 (4): 597–648. arXiv:1210.5658. doi:10.1090/S0273-0979-2014-01456-9.
Grayson, Daniel R. (2018). "An introduction to univalent foundations for mathematicians". Bulletin of the American Mathematical Society. 55 (4): 427–450. arXiv:1711.01477. doi:10.1090/bull/1616. S2CID 32293255.
Vladimir Voevodsky (2014) Experimental library of univalent formalization of mathematics
Kapulkin, Chris; Lumsdaine, Peter LeFanu; Voevodsky, Vladimir (2012). "The Simplicial Model of Univalent Foundations". arXiv:1211.2851 [math.LO].
Shulman, Michael (2015). "Univalence for inverse diagrams and homotopy canonicity". Mathematical Structures in Computer Science. 25 (5): 1203–1277. arXiv:1203.3253. doi:10.1017/S0960129514000565. S2CID 13595170.
Martín Hötzel Escardó (October 18, 2018) A self-contained, brief and complete formulation of Voevodsky’s Univalence Axiom

chalmers.se

cse.chalmers.se

Coquand's Bourbaki Lecture Paper and Video
Coquand (2014) part 1
Coquand (2014) part 2
Bezem, M.; Coquand, T.; Huber, S. "A model of type theory in cubical sets" (PDF).

cmu.edu

andrew.cmu.edu

Awodey, Steve (2014). "Structuralism, Invariance, and Univalence" (PDF). Philosophia Mathematica. 22 (1): 1–11. CiteSeerX 10.1.1.691.8113. doi:10.1093/philmat/nkt030.

repository.cmu.edu

Awodey, Steven; Bauer, Andrej (2004). "Propositions as [types]". J. Log. Comput. 14 (4): 447–471. doi:10.1093/logcom/14.4.447.

doi.org

Awodey, Steve (2014). "Structuralism, Invariance, and Univalence" (PDF). Philosophia Mathematica. 22 (1): 1–11. CiteSeerX 10.1.1.691.8113. doi:10.1093/philmat/nkt030.
Awodey, Steven; Bauer, Andrej (2004). "Propositions as [types]". J. Log. Comput. 14 (4): 447–471. doi:10.1093/logcom/14.4.447.
See Ahrens, Benedikt; Kapulkin, Chris; Shulman, Michael (2015). "Univalent categories and the Rezk completion". Mathematical Structures in Computer Science. 25 (5): 1010–1039. arXiv:1303.0584. doi:10.1017/S0960129514000486. S2CID 1135785.
Pelayo, Álvaro; Warren, Michael A. (2014). "Homotopy type theory and Voevodsky's univalent foundations". Bulletin of the American Mathematical Society. 51 (4): 597–648. arXiv:1210.5658. doi:10.1090/S0273-0979-2014-01456-9.
Grayson, Daniel R. (2018). "An introduction to univalent foundations for mathematicians". Bulletin of the American Mathematical Society. 55 (4): 427–450. arXiv:1711.01477. doi:10.1090/bull/1616. S2CID 32293255.
Shulman, Michael (2015). "Univalence for inverse diagrams and homotopy canonicity". Mathematical Structures in Computer Science. 25 (5): 1203–1277. arXiv:1203.3253. doi:10.1017/S0960129514000565. S2CID 13595170.

github.com

Foundations library, see https://github.com/vladimirias/Foundations
UniMath library, see https://github.com/UniMath/UniMath
HoTT Coq library, see https://github.com/HoTT/HoTT
HoTT Agda library, see https://github.com/HoTT/HoTT-Agda

ias.edu

math.ias.edu

Voevodsky, Vladimir (September 9–10, 2014). "Foundations of mathematics — their past, present and future". The 2014 Paul Bernays Lectures. ETH Zurich. See item 11 at Voevodsky Lectures
V. Voevodsky, Univalent Foundations Project (a modified version of an NSF grant application), p. 9

mcgill.ca

math.mcgill.ca

Makkai, M. (1995). "First Order Logic with Dependent Sorts, with Applications to Category Theory" (PDF). FOLDS.

ncatlab.org

univalence axiom in nLab

nott.ac.uk

cs.nott.ac.uk

Altenkirch, Thorsten; Kaposi, Ambrus, A syntax for cubical type theory (PDF)

psu.edu

citeseerx.ist.psu.edu

Awodey, Steve (2014). "Structuralism, Invariance, and Univalence" (PDF). Philosophia Mathematica. 22 (1): 1–11. CiteSeerX 10.1.1.691.8113. doi:10.1093/philmat/nkt030.

semanticscholar.org

api.semanticscholar.org

See Ahrens, Benedikt; Kapulkin, Chris; Shulman, Michael (2015). "Univalent categories and the Rezk completion". Mathematical Structures in Computer Science. 25 (5): 1010–1039. arXiv:1303.0584. doi:10.1017/S0960129514000486. S2CID 1135785.
Grayson, Daniel R. (2018). "An introduction to univalent foundations for mathematicians". Bulletin of the American Mathematical Society. 55 (4): 427–450. arXiv:1711.01477. doi:10.1090/bull/1616. S2CID 32293255.
Shulman, Michael (2015). "Univalence for inverse diagrams and homotopy canonicity". Mathematical Structures in Computer Science. 25 (5): 1203–1277. arXiv:1203.3253. doi:10.1017/S0960129514000565. S2CID 13595170.