This site serves to collect and disseminate research, resources, and tools for the investigation of homotopy type theory, and hosts a blog for those involved in its study. Homotopy Type Theory refers to a new field of study relating Martin-Löf’s system of intensional, constructive type theory with abstract homotopy theory. Propositional equality is interpreted as…
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Homotopy Type Theory | homotopytypetheory.org Reviews
https://homotopytypetheory.org
This site serves to collect and disseminate research, resources, and tools for the investigation of homotopy type theory, and hosts a blog for those involved in its study. Homotopy Type Theory refers to a new field of study relating Martin-Löf’s system of intensional, constructive type theory with abstract homotopy theory. Propositional equality is interpreted as…
homotopytypetheory.org
Homotopy Theory | Homotopy Type Theory
https://homotopytypetheory.org/category/homotopy-theory
Category Archives: Homotopy Theory. Universal Properties of Truncations. Some days ago at the HoTT/UF workshop in Warsaw (which was a great event! I have talked about functions out of truncations. I have focussed on the propositional truncation , and I want to write this blog post in case … Continue reading →. Double Groupoids and Crossed Modules in HoTT. The torus is the product of two circles, cubically. Splitting Idempotents, II. This post is an answer to that question. One of the fundamental construc...
Code | Homotopy Type Theory
https://homotopytypetheory.org/coq
An intensional dependent type theory called the Calculus of Inductive Constructions (CIC) has implementations in proof assistants such as Coq. The Martin-Lof type theory can be seen as a fragment of CIC. The standard univalent model that allows one to use MLTT to formalize abstract mathematics in the univalent style has been informally checked to extend to some of the subsets of CIC. This situation led to the development of two different approaches to univalent formalization of mathematics in Coq and Agda.
The HoTT Book | Homotopy Type Theory
https://homotopytypetheory.org/book
Univalent Foundations of Mathematics. The Univalent Foundations Program. Institute for Advanced Study. Buy a hardcover copy for $22.05. 620 pages, 6″ 9″ size, hardcover]. Buy a paperback copy for $9.73. 620 pages, 6″ 9″ size, paperback]. Download PDF for on-screen viewing. 490 pages, letter size, in color, with color links]. Download PDF for e-books. 622 pages, size 6″ 9″, small margins, black and white]. Download PDF for printing on letter paper. Download PDF for printing on A4 paper. While the page num...
The HoTT Book | Homotopy Type Theory
https://homotopytypetheory.org/2013/06/20/the-hott-book
Homotopy Theory in Type Theory: Progress Report. This posting is the official announcement of The HoTT Book. Homotopy Type Theory: Univalent Foundations of Mathematics. The Univalent Foundations Program, Institute for Advanced Study. The book is the result of an amazing collaboration between virtually everyone involved in the Univalent Foundations Program at the IAS last year. It contains the state of the art in HoTT as an informal foundation of mathematics, and that requires a bit of explanation. In it:...
Homotopy Type Theory should eat itself (but so far, it’s too big to swallow) | Homotopy Type Theory
https://homotopytypetheory.org/2014/03/03/hott-should-eat-itself
Composition is not what you think it is! Why “nearly invertible” isn’t. Eilenberg-MacLane Spaces in HoTT →. Homotopy Type Theory should eat itself (but so far, it’s too big to swallow). The title of this post is an homage to a well-known paper by James Chapman called. Type theory should eat itself. I also considered titling the post. How I spent my Christmas vacation trying to construct semisimplicial types in a way that I should have known in advance wasn’t going to work. Universe is a model of HoTT with.
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FOM discussion | Formalized Mathematics
https://slawekk.wordpress.com/2014/10/25/fom-discussion
Just another WordPress.com weblog. Laquo; IsarMathLib 1.9.2 released. There is a very interesting discussion. About formalized mathematics going on the Foundations of Mathematics mailing list. The most interesting part of it (at least to me) is the thread about relative merits of Homotopy Type Theory. About this in the Bulletin of the American Mathematical Society. Here is a very simple statement which I often give to students as a first exercise in iteration, and to practice formal mathematics. This was...
Homotopy type theory | Mathematics and Computation
http://math.andrej.com/category/homotopy-type-theory
Category Archives: Homotopy type theory. The real numbers in homotopy type theory (CCA 2016 slides). June 15, 2016. I am about to give an invited talk at the Computability and Complexity in Analysis 2016. Conference (yes, I am in the south of Portugal, surrounded by loud English tourists, but we. Working here, in a basement no less). Here are the slides, with extensive speaker notes, comment and questions are welcome. View all 6 comments. A HoTT PhD position in Ljubljana. November 22, 2014. The student w...
Software | Mathematics and Computation
http://math.andrej.com/category/software
November 7, 2015. My student Marko Koležnik. Is about to finish his Master’s degree in Mathematics at the University of Ljubljana. He implemented Agda Writer. A graphical user interface for the Agda proof assistant on the OS X platform. As he puts it, the main advantage of Agda Writer is. But the list of cool features is a bit longer:. It comes with preinstalled Agda so there is zero installation effort. Of course, you can use your own Agda as well). Clickable error messages and goals. View all 5 comments.
Eff | Mathematics and Computation
http://math.andrej.com/category/programming/eff
A HoTT PhD position in Ljubljana. November 22, 2014. I am looking for a PhD student in mathematics. Full tuition and stipend will be provided for a period of three years, which is also the official length of the programme. The topic of research is somewhat flexible and varies from constructive models of homotopy type theory to development of a programming language for a proof assistant based on dependent type theory, see the short summary of the Effmath project. For a more detailed description. So you wo...
The troublesome reflection rule (TYPES 2015 slides) | Mathematics and Computation
http://math.andrej.com/2015/05/19/the-troublesome-reflection-rule-types-2015-slides
The troublesome reflection rule (TYPES 2015 slides). May 19, 2015. Here are the slides of my TYPES 2015. Talk “The troublesome reflection rule” with fairly detailed presenter notes. The meeting is taking place in Tallinn, Estonia a very cool country in many senses (it’s not quite spring yet even though we’re in the second half of May, and it’s the country that gave us Skype). The troublesome reflection rule (TYPES 2015). Another PhD position in Ljubljana. Intermediate truth values →. May 21, 2015 at 21:31.
Semantic Domain: February 2015
http://semantic-domain.blogspot.com/2015_02_01_archive.html
Thursday, February 26, 2015. Midlands Graduate School 2015. Registration for the Midlands Graduate School. I'll be lecturing again this year on functional reactive programming, and am very much looking forward to meeting the participants. The Midlands Graduate School in the Foundations of Computing Science (MGS). This year's MGS is hosted by the Department of Computer Science. At the University of Sheffield. It will start on April 07 and finish on April 11. Roy Crole, Leicester. Jeremy Gibbons, Oxford.
FORM & FORMALISM: FORM & FORMALISM III: FORMALISATION & DIALECTICS
http://formandformalism.blogspot.com/2012/05/form-formalism-iii-formalisation.html
Thursday, May 17, 2012. FORM and FORMALISM III: FORMALISATION and DIALECTICS. On June 7th and 8th, at the JVE in Maastricht, the Netherlands, the third Form and Formalism. Conference will be taking place, under the title Formalisation and Dialectics. Pasted below are the manifesto, schedule and poster for the conference (designed by Mary Ikoniadou). In 1812, and Boole’s. Mathematical Analysis of Logic. Has been meek. The two traditions issuing from the logical revolts of the nineteenth century –...
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The Homotopian
Liberty, Equality, Universal Skin Care. Tuesday, December 29, 2009. The Rise of the Republican Woman. AC Kleinheider has an interesting article on the phenomenon of the emergence of Republican women. After all, the party's anti-slavery platform was the inspiration for Susan B. Anthony and Elizabeth Cady Stanton's women's suffrage movement and many of the same people involved in the abolition movement were also involved in women's suffrage. Links to this post. Wednesday, December 2, 2009. The movement for...
Motivic stuff
Cohomology, homotopy theory, and arithmetic geometry. AMS Grad student blog. 8220;Secret” notes of Grothendieck to be digitized. Posted by Andreas Holmstrom on June 18, 2015. Apparently the archive of Grothendieck’s “scribbles” left at Montpellier are now in the process of being digitized and made available online. A tiny collection of 20 000 pages! Latest news on the Global Digital Library for Mathematics Research. Posted by Andreas Holmstrom on July 19, 2014. See this brief note in the AMS Notices.
Homotopy Type Theory
Homotopy Type Theory and Univalent Foundations. This site serves to collect and disseminate research, resources, and tools for the investigation of homotopy type theory, and hosts a blog for those involved in its study. Univalent Foundations of Mathematics. Is Vladimir Voevodsky’s new program for a comprehensive, computational foundation for mathematics based on the homotopical interpretation of type theory. The type theoretic. Homotopy Type Theory and Univalent Foundations. 20 March 2011 at 11:23.
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