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Homotopies, equivalences, sets, and propositions #14

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merged 15 commits into from
Dec 13, 2023

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@Anatolay Anatolay commented Sep 27, 2023

This PR contains the following:

  • Most of Section 2.4 Homotopies and equivalences
  • Most of Section 2.6 Cartesian product types
  • Section 2.8 The unit type
  • Definition of functional extensionality in Section 2.9 $\prod$-types and the function extensionality axiom
  • Some of Section 3.1 Sets and $n$-types
    • Definition of isSet
    • Proofs that Unit, products of sets, and functions into sets are sets
    • Simplification of proofs by factoring out injective-equivalence lemma
  • Some of Section 3.3 Mere propositions
    • Proofs that Unit and functions into mere propositions are mere propositions
  • Definition of contractibility in Section 3.11 Contractibility

Original description:

Definitions and proofs for Section 2.4.

Depends on #11

@Anatolay Anatolay marked this pull request as ready for review December 13, 2023 11:30
@fizruk fizruk force-pushed the 2.4-homotopies-are-equivalences branch from de0dc3c to 035135b Compare December 13, 2023 11:37
@fizruk fizruk changed the title 2.4 homotopies are equivalences Homotopies, equivalences, sets, and propositions Dec 13, 2023
@fizruk fizruk merged commit 463d91e into main Dec 13, 2023
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@fizruk fizruk deleted the 2.4-homotopies-are-equivalences branch December 13, 2023 23:24
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4 participants