Homotopy Type Theory For Dummies

More documents

Recommendations

Info

Homotopic interpretation J in the <strong>Homotopy</strong> interpretation To show Π p:a=a (a, p) = Σx:A x=a (a, refl(a)) we use Π (b,p):Σb:A,a=b (a, refl(a)) = (b, p) Thorsten Altenkirch (Nottingham) Edinburgh 13 October 30, 2013 12 / 29
The univalence axiom Univalence Rejection of UIP is not the only thing the <strong>Homotopy</strong> interpretation is good for. It also suggests an additional principle: the univalence axiom. This axiom can also be justified from a purely logical perspective. And it is inconsistent with UIP! Thorsten Altenkirch (Nottingham) Edinburgh 13 October 30, 2013 13 / 29
Page 1 and 2: Homotopy Type Theory For Dummies Th
Page 3 and 4: Basic Type Theory Type Theory 101 M
Page 5 and 6: Identity types Identity types Given
Page 7 and 8: Identity types Should equality be p
Page 9 and 10: Homotopic interpretation Uniqueness
Page 11: Homotopic interpretation While we c
Page 15 and 16: The univalence axiom What is the eq
Page 17 and 18: Truncation levels Truncation levels
Page 19 and 20: Truncation levels The Truncation Hi
Page 21 and 22: HITs Higher inductive types There a
Page 23 and 24: HITs Higher inductive types This al
Page 25 and 26: HITs Truncations We can use HITs to
Page 27 and 28: Metatheory Constructive models The
Page 29: Computer Science ? The HoTT people

Homotopy Type Theory For Dummies

Create successful ePaper yourself

Delete template?

Save as template?