Homotopy type theory (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Homotopy type theory" in English language version.

refsWebsite

Global rank English rank

9arxiv.org

69^th place

59^th place

9doi.org

2^nd place

7semanticscholar.org

11^th place

8^th place

5github.com

383^rd place

320^th place

5homotopytypetheory.org

low place

3cmu.edu

1,564^th place

1,028^th place

2ams.org

451^st place

277^th place

2loria.fr

low place

2acm.org

1,185^th place

840^th place

1ieee.org

652^nd place

515^th place

1books.google.com

3^rd place

1ucalgary.ca

3,395^th place

2,576^th place

1mawarren.net

low place

1uu.se

3,805^th place

3,371^st place

1mq.edu.au

low place

7,448^th place

1archive.today

14^th place

1harvard.edu

18^th place

17^th place

1ucr.edu

1,553^rd place

1,008^th place

1web.archive.org

1^st place

1rett.org.uk

low place

1files.wordpress.com

869^th place

864^th place

1ncatlab.org

low place

8,775^th place

1ias.edu

7,948^th place

5,350^th place

1utexas.edu

916^th place

706^th place

1andrej.com

low place

1computingreviews.com

low place

1rdworldonline.com

low place

1archives-ouvertes.fr

1,031^st place

879^th place

acm.org

cacm.acm.org

Monroe, D (2014). "A New Type of Mathematics?". Comm ACM. 57 (2): 13–15. doi:10.1145/2557446. S2CID 6120947.

dl.acm.org

Sojakova, Kristina (2015). Higher Inductive Types as Homotopy-Initial Algebras. POPL 2015. arXiv:1402.0761. doi:10.1145/2676726.2676983.

ams.org

mathscinet.ams.org

Hofmann, Martin; Streicher, Thomas (1998). "The groupoid interpretation of type theory". In Sambin, Giovanni; Smith, Jan M. (eds.). Twenty Five Years of Constructive Type Theory. Oxford Logic Guides. Vol. 36. Clarendon Press. pp. 83–111. ISBN 978-0-19-158903-4. MR 1686862.
Ahrens, Benedikt; Kapulkin, Krzysztof; 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. MR 3340533. S2CID 1135785.

andrej.com

math.andrej.com

Bauer, Andrej (20 June 2013). "The HoTT Book". Mathematics and Computation. Retrieved 6 June 2021.

archive.today

"86th edition of the Peripatetic Seminar on Sheaves and Logic, Henri Poincaré University, September 8-9, 2007". loria.fr. Archived from the original on 17 December 2014. Retrieved 20 December 2014.

archives-ouvertes.fr

hal-iogs.archives-ouvertes.fr

Cohen, Cyril; Coquand, Thierry; Huber, Simon; Mörtberg, Anders (2015). Cubical Type Theory: a constructive interpretation of the univalence axiom. TYPES 2015.

arxiv.org

Shulman, Michael (27 January 2016). "Homotopy Type Theory: A synthetic approach to higher equalities". arXiv:1601.05035v3 [math.LO]., footnote 1
Ahrens, Benedikt; Kapulkin, Krzysztof; 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. MR 3340533. S2CID 1135785.
Berg, Benno van den; Garner, Richard (27 July 2010). "Topological and simplicial models of identity types". arXiv:1007.4638 [math.LO].
Lumsdaine, Peter LeFanu; Warren, Michael A. (6 November 2014). "The local universes model: an overlooked coherence construction for dependent type theories". ACM Transactions on Computational Logic. 16 (3): 1–31. arXiv:1411.1736. doi:10.1145/2754931. S2CID 14068103.
Awodey, Steve; Warren, Michael A. (3 September 2007). "Homotopy theoretic models of identity types". Mathematical Proceedings of the Cambridge Philosophical Society. 146 (1): 45. arXiv:0709.0248. Bibcode:2008MPCPS.146...45A. doi:10.1017/S0305004108001783. S2CID 7915709.
van den Berg, Benno; Garner, Richard (1 December 2007). "Types are weak omega-groupoids". Proceedings of the London Mathematical Society. 102 (2): 370–394. arXiv:0812.0298. doi:10.1112/plms/pdq026. S2CID 5575780.
Martín Hötzel Escardó (October 18, 2018) A self-contained, brief and complete formulation of Voevodsky’s Univalence Axiom
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.
Sojakova, Kristina (2015). Higher Inductive Types as Homotopy-Initial Algebras. POPL 2015. arXiv:1402.0761. doi:10.1145/2676726.2676983.

books.google.com

Hofmann, Martin; Streicher, Thomas (1998). "The groupoid interpretation of type theory". In Sambin, Giovanni; Smith, Jan M. (eds.). Twenty Five Years of Constructive Type Theory. Oxford Logic Guides. Vol. 36. Clarendon Press. pp. 83–111. ISBN 978-0-19-158903-4. MR 1686862.

cmu.edu

cs.cmu.edu

Licata, Daniel R.; Harper, Robert (21 July 2011). "Canonicity for 2-Dimensional Type Theory" (PDF). Carnegie Mellon University. Retrieved 6 June 2021.
Anguili, Carlo; Favonia; Harper, Robert (2018). Cartesian Cubical Computational Type Theory: Constructive Reasoning with Paths and Equalities (PDF). Computer Science Logic 2018. Retrieved 26 August 2018. (to appear)

andrew.cmu.edu

[1] Steve Awodey. Univalence as a principle of logic. Indagationes Mathematicae: Special Issue L.E.J. Brouwer, 50 years later, D. van Dalen, et al. (ed.s), 2018. Preprint.

computingreviews.com

ACM Computing Reviews. "Best of 2013".

doi.org

Hofmann, M.; Streicher, T. (1994). "The groupoid model refutes uniqueness of identity proofs". Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science. pp. 208–212. doi:10.1109/LICS.1994.316071. ISBN 0-8186-6310-3. S2CID 19496198.
Ahrens, Benedikt; Kapulkin, Krzysztof; 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. MR 3340533. S2CID 1135785.
Lumsdaine, Peter LeFanu; Warren, Michael A. (6 November 2014). "The local universes model: an overlooked coherence construction for dependent type theories". ACM Transactions on Computational Logic. 16 (3): 1–31. arXiv:1411.1736. doi:10.1145/2754931. S2CID 14068103.
Awodey, Steve; Warren, Michael A. (3 September 2007). "Homotopy theoretic models of identity types". Mathematical Proceedings of the Cambridge Philosophical Society. 146 (1): 45. arXiv:0709.0248. Bibcode:2008MPCPS.146...45A. doi:10.1017/S0305004108001783. S2CID 7915709.
van den Berg, Benno; Garner, Richard (1 December 2007). "Types are weak omega-groupoids". Proceedings of the London Mathematical Society. 102 (2): 370–394. arXiv:0812.0298. doi:10.1112/plms/pdq026. S2CID 5575780.
Awodey, Steve; Garner, Richard; Martin-Löf, Per; Voevodsky, Vladimir (27 February – 5 March 2011). "Mini-Workshop: The Homotopy Interpretation of Constructive Type Theory" (PDF). Oberwolfach Reports. 8. Mathematical Research Institute of Oberwolfach: 609–638. doi:10.4171/OWR/2011/11. Retrieved 6 June 2021.
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.
Monroe, D (2014). "A New Type of Mathematics?". Comm ACM. 57 (2): 13–15. doi:10.1145/2557446. S2CID 6120947.
Sojakova, Kristina (2015). Higher Inductive Types as Homotopy-Initial Algebras. POPL 2015. arXiv:1402.0761. doi:10.1145/2676726.2676983.

files.wordpress.com

hottheory.files.wordpress.com

Awodey, Steve; Garner, Richard; Martin-Löf, Per; Voevodsky, Vladimir (27 February – 5 March 2011). "Mini-Workshop: The Homotopy Interpretation of Constructive Type Theory" (PDF). Oberwolfach Reports. 8. Mathematical Research Institute of Oberwolfach: 609–638. doi:10.4171/OWR/2011/11. Retrieved 6 June 2021.

github.com

Notes on homotopy lambda calculus, March 2006
GitHub repository, Univalent Mathematics
GitHub repository, Andrej Bauer, Homotopy theory in Coq
Bauer, Andrej; Voevodsky, Vladimir (29 April 2011). "Basic homotopy type theory". GitHub. Retrieved 6 June 2021.
GitHub repository, Homotopy type theory

harvard.edu

ui.adsabs.harvard.edu

Awodey, Steve; Warren, Michael A. (3 September 2007). "Homotopy theoretic models of identity types". Mathematical Proceedings of the Cambridge Philosophical Society. 146 (1): 45. arXiv:0709.0248. Bibcode:2008MPCPS.146...45A. doi:10.1017/S0305004108001783. S2CID 7915709.

homotopytypetheory.org

Homotopy Type Theory and Univalent Foundations Blog
Homotopy Type Theory blog
Type Theory and Univalent Foundations
Univalent Foundations Program (2013). Homotopy Type Theory: Univalent Foundations of Mathematics. Institute for Advanced Study.
Official announcement of The HoTT Book, by Steve Awodey, 20 June 2013

ias.edu

math.ias.edu

IAS school of mathematics: Special Year on The Univalent Foundations of Mathematics

ieee.org

ieeexplore.ieee.org

Hofmann, M.; Streicher, T. (1994). "The groupoid model refutes uniqueness of identity proofs". Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science. pp. 208–212. doi:10.1109/LICS.1994.316071. ISBN 0-8186-6310-3. S2CID 19496198.

loria.fr

"86th edition of the Peripatetic Seminar on Sheaves and Logic, Henri Poincaré University, September 8-9, 2007". loria.fr. Archived from the original on 17 December 2014. Retrieved 20 December 2014.
Preliminary list of PSSL86 participants

mawarren.net

Warren, Michael A. (2006). Homotopy Models of Intensional Type Theory (PDF) (Thesis).

mq.edu.au

comp.mq.edu.au

Richard Garner, Factorisation axioms for type theory

ncatlab.org

Homotopy Type Theory: References

rdworldonline.com

Meyer, Florian (3 September 2014). "A new foundation for mathematics". R&D Magazine. Retrieved 29 July 2021.

rett.org.uk

lib.rett.org.uk

Lumsdaine, Peter (2010). "Higher Categories from Type Theories" (PDF) (Ph.D.). Carnegie Mellon University. Archived from the original (PDF) on 21 December 2014. Retrieved 21 December 2014.

semanticscholar.org

api.semanticscholar.org

Hofmann, M.; Streicher, T. (1994). "The groupoid model refutes uniqueness of identity proofs". Proceedings Ninth Annual IEEE Symposium on Logic in Computer Science. pp. 208–212. doi:10.1109/LICS.1994.316071. ISBN 0-8186-6310-3. S2CID 19496198.
Ahrens, Benedikt; Kapulkin, Krzysztof; 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. MR 3340533. S2CID 1135785.
Lumsdaine, Peter LeFanu; Warren, Michael A. (6 November 2014). "The local universes model: an overlooked coherence construction for dependent type theories". ACM Transactions on Computational Logic. 16 (3): 1–31. arXiv:1411.1736. doi:10.1145/2754931. S2CID 14068103.
Awodey, Steve; Warren, Michael A. (3 September 2007). "Homotopy theoretic models of identity types". Mathematical Proceedings of the Cambridge Philosophical Society. 146 (1): 45. arXiv:0709.0248. Bibcode:2008MPCPS.146...45A. doi:10.1017/S0305004108001783. S2CID 7915709.
van den Berg, Benno; Garner, Richard (1 December 2007). "Types are weak omega-groupoids". Proceedings of the London Mathematical Society. 102 (2): 370–394. arXiv:0812.0298. doi:10.1112/plms/pdq026. S2CID 5575780.
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.
Monroe, D (2014). "A New Type of Mathematics?". Comm ACM. 57 (2): 13–15. doi:10.1145/2557446. S2CID 6120947.

ucalgary.ca

pages.cpsc.ucalgary.ca

"Foundational Methods in Computer Science 2006, University of Calgary, June 7th - 9th, 2006". University of Calgary. Retrieved 6 June 2021.

ucr.edu

math.ucr.edu

Voevodsky, Vladimir (27 September 2006). "A very short note on homotopy λ-calculus". ucr.edu. Retrieved 6 June 2021.

utexas.edu

golem.ph.utexas.edu

Shulman, Mike (20 June 2013). "The HoTT Book". The n-Category Café. Retrieved 6 June 2021 – via University of Texas.

uu.se

www2.math.uu.se

"Identity Types - Topological and Categorical Structure, Workshop, Uppsala, November 13-14, 2006". Uppsala University - Department of Mathematics. Retrieved 6 June 2021.

web.archive.org

Lumsdaine, Peter (2010). "Higher Categories from Type Theories" (PDF) (Ph.D.). Carnegie Mellon University. Archived from the original (PDF) on 21 December 2014. Retrieved 21 December 2014.