Mini-HoTT
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Table of Contents

  • Quick start
  • Everything in Mini HoTT
  • Types
  • Other custom types
  • Basic functions
  • Decidable equality
  • Algebra of paths
  • Properties on the groupoid
  • Algebra of Pathovers
  • Transport
  • Transport Lemmas
  • Action on dependent paths
  • Coproduct identities
  • When ∑ and ∏ commute
  • Fibre type
  • Transport with fibers
  • Homotopies
  • Composition with homotopies
  • Naturality
  • Equivalences
  • Quasiinverses
  • Quasiinverse Lemmas
  • Biinverses
  • Half-adjoints
  • Equivalence reasoning
  • Basic Equivalences
  • Equivalence with Pi type
  • Equivalences preserved by Sigma types
  • Sigma equivalences
  • Voevodsky’s Univalence Axiom
  • Function extensionality
  • Univalence lemmas
  • Univalence Lemma for Identity equivalence
  • Transport and Univalence
  • Function extensionality transport case
  • Dependent function extensionality transport case
  • Hlevel types
  • Hedberg theorem
  • HLevel Lemmas
  • Types of Morphisms
  • Rewriting
  • Set truncations
  • Groupoid truncations
  • Product identities
  • Suspensions
  • Intervals
  • Propositional truncation
  • Quotient type
  • Circles
  • Fundamental group
  • Monoids
  • Relation
  • Integers
  • Groups
  • The type of natural numbers
  • Connectedness
  • The Axiom Of Choice
Mini-HoTT
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