Homotopy Type Theory For Dummies

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Computer Science ? Why should we care? Structures can be 1st class citizens. (equality is isomorphism) HITs provide better ways to define the Cauchy Reals and the constructible hierarchy (avoiding choice). Quotient containers (like multisets) become ordinary containers. Thorsten Altenkirch (Nottingham) Edinburgh 13 October 30, 2013 28 / 29
Computer Science ? The HoTT people Thorsten Altenkirch (Nottingham) Edinburgh 13 October 30, 2013 29 / 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 and 12: Homotopic interpretation While we c
Page 13 and 14: The univalence axiom Univalence Rej
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: Metatheory Constructive models The

Homotopy Type Theory For Dummies

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