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Homotopytypetheory.org Server Location

Country: United States
Metropolitan Area: San Francisco
Postal Reference Code: 94110
Latitude: 37.7506
Longitude: -122.4121




Summarized Content

This site serves to collect and disseminate research, resources, and tools for the investigation of homotopy type theory, and hosts a blog abstract homotopy theory.  Propositional equality is interpreted as homotopy and type isomorphism as homotopy equivalence. Logical constructions in type theory then correspond to homotopy-invariant constructions on spaces, while theorems and even proofs in the logical system inherit a homotopical meaning.  As the natural logic of homotopy, constructive type theory is also related to higher category universe with homotopy equivalence of small types. The program is currently being implemented with the help of the automated proof as*istant Coq.  The Univalent Foundations program is closely tied to homotopy type theory and is being pursued in parallel by many of the


Homotopytypetheory Main Page Content

HTML Tag Content Informative?
Title: Homotopy Type Could be improved
Description: 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
H1: Homotopy Type TheoryIs it informative enough?
H2: Homotopy Type Theory and Univalent Foundations
H3: One Response to Homotopy Type Theory and Univalent Foundations

Other Helpful Websites and Services for Homotopytypetheory

Internal Pages

/about/feed/:
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Comments on: Homotopy Type Theory and Univalent Foundations

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/coq/:
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Code | Homotopy Type Theory

Description

An intensional dependent type theory called the Calculus of Inductive Constructions (CIC) has implementations in proof istants such as Coq and Agda. 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…

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/events/:
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Events | Homotopy Type Theory

Description

Here are some past HoTT events. The Institute for Advanced Study had a year-long special program devoted to the Univalent Foundations Program in 2012-13.  See the list of Participants here.  See the Wiki here. May 8 -- 11, 2013, there was a special session on Univalent Foundations at the North American Annual Meeting of the ociation for Symbolic…

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Events

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/links/:
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Links | Homotopy Type Theory

Description

Introductory videos, talks, and blog posts A series of introductory talks on the Univalent Foundations Program were given at the IAS in December 2010. The talks can be viewed here, and among them are the following talks: Steve Awodey, Constructive type theory and homotopy. Andrew Appel, Introduction to the Coq proof istant. Vladimir Voevodsky, Univalent foundations…

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Introductory videos, talks, and blog posts

/references/:
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References | Homotopy Type Theory

Description

The list of references below is now superseded by the catalog of references on our wiki. Please refer to that catalog instead, and feel free to edit the information there. The list below is preserved for historical reasons, and is not up to date.   A roughly taxonomised listing of some of the papers on Homotopy Type…

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References

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