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Tübingen Study Group for Homotopy Type Theory

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HoTT-StudyGroup

Tübingen Study Group for Homotopy Type Theory

This repository is used for coordinating the Study Group on Homotopy Type Theory in Tübingen and to share articles, links, books, dates, etc...

##Doodle Poll

Insert your available time slots in the doodle poll: Doodle [We have now settled on the Monday Tuesday 14-16 timeslot.]

##Schedule The meetings will take place on Mondays Tuesdays at 14:1514:00 in room A302 C109 at the Sand. The preliminary schedule looks as follows:

  • 13 Dec 2016 : Organisation of the Reading Group, Backgrounds in Type theory, Introduction to Martin-Löf dependent type theory and its identity types. (David + Ingo)

In the first meeting we discussed:

  1. The two kinds of judgments of Martin-Löf type theory.
  2. The FIEC-Schema for introducing new types (Formation, Introduction, Elimination, Computation Rules).
  3. Nondependent Product and Sum Types.
  4. Dependent Function Type (= Pi Type) and Dependent Product Type (= Sigma Type).
  5. The Type of natural numbers.
  6. The provability of the type-theoretic version of the Axiom of Choice.
  • 20 Dec 2016 : We will discuss chapter 1 of the HoTT book, wrap up the remaining questions about the dependent function + product types and probably concentrate on the Identity-Type (propositional Identity) (Ingo)

We discussed:

  1. The FIEC rules for the identity type.
  2. How the Elimination principle for the identity type does not allow us to deduce the Uniqueness of Identity Proofs (UIP) property.
  3. How to strengthen the identity type with Streicher's axiom K so that UIP is deducible.
  4. The interpretation of the Identity Type as the Type of Paths in a topological space. (And the type of paths between these paths as the homotopies between the paths)
  5. Two examples of Higher Inductive Types: The circle S1 and the Type of Natural numbers mod 2.

See also: Dan Licata on Identity Types

  • 10 Jan 2017 : We will discuss from Chapter 2 the beginning until section 2.4 inclusive. (Philipp)

Groupoids and Puzzles Alan Weinstein on Groupoids (PDF)

  • 17 Jan 2017:
  • 24 Jan 2017:
  • 31 Jan 2017 :

Links

Computer Implementations of HoTT

  • Coq Library on Github: Github
  • Agda Library on Github: Github
  • Lean 0.2 Library on Github: Github

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Tübingen Study Group for Homotopy Type Theory