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
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