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:
- The two kinds of judgments of Martin-Löf type theory.
- The FIEC-Schema for introducing new types (Formation, Introduction, Elimination, Computation Rules).
- Nondependent Product and Sum Types.
- Dependent Function Type (= Pi Type) and Dependent Product Type (= Sigma Type).
- The Type of natural numbers.
- 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:
- The FIEC rules for the identity type.
- How the Elimination principle for the identity type does not allow us to deduce the Uniqueness of Identity Proofs (UIP) property.
- How to strengthen the identity type with Streicher's axiom K so that UIP is deducible.
- 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)
- 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 :
- The official HoTT Book: HoTT Book
- Robert Harper's Video Lectures: Lectures
- nLab Article: nLab
- Wikipedia Article: Wikipedia
- Video List from the Fields Institute Workshop: Fields Institute