Mini-HoTT is a basic Agda library which contains basic definitions and results in Univalent type theory. There is no guarantee whatsoever of any kind. At the moment, this library suffers of many changes without any warning.

• Website documentation: https://mini-hott.readthedocs.io/

The library should work with the Agda latest version, and it tested with (v 2.6.1).

$ git clone http://github.com/jonaprieto/mini-hott

For newcomers, the easiest way to install a library is using agda-pkg

You can run the following commands to install it:

$ pip3 install agda-pkg
$ apkg init
$ apkg install --github jonaprieto/mini-hott

After installing the sources, include at the top of your file the following line:

open import MiniHoTT

.. toctree::
   :caption: Table of Contents
   :maxdepth: 2

   src/Intro
   src/MiniHoTT
   src/BasicTypes
   src/BasicFunctions
   src/DecidableEquality
   src/AlgebraOnPaths
   src/AlgebraOnDependentPaths
   src/Transport
   src/TransportLemmas
   src/CoproductIdentities
   src/DependentAlgebra
   src/FibreType
   src/HomotopyType
   src/HomotopyLemmas
   src/EquivalenceType
   src/QuasiinverseType
   src/QuasiinverseLemmas
   src/BiinverseEquivalenceType
   src/HalfAdjointType
   src/EquivalenceReasoning
   src/BasicEquivalences
   src/PiPreserves
   src/SigmaPreserves
   src/SigmaEquivalence
   src/UnivalenceAxiom
   src/FunExtAxiom
   src/UnivalenceLemmas
   src/UnivalenceIdEquiv
   src/UnivalenceTransport
   src/FunExtTransport
   src/FunExtTransportDependent
   src/HLevelTypes
   src/HedbergLemmas
   src/HLevelLemmas
   src/TypesofMorphisms
   src/SectionsAndRetractions
   src/Rewriting
   src/SetTruncationType
   src/ProductIdentities
   src/SuspensionType
   src/IntervalType
   src/TruncationType
   src/QuotientType
   src/CircleType
   src/FundamentalGroupType
   src/MonoidType
   src/RelationType
   src/IntegerType
   src/GroupType
   src/NaturalType
   src/Connectedness
   src/TheAxiomOfChoice

• Theory
  • The Univalent Foundations Program. Homotopy Type Theory: Univalent Foundations of Mathematics. 2013.
  • The Homotopy Type Theory and Univalent Foundations CAS project. Symmetry Book. 2020.
  • Escardo, M. Introduction to Univalent Foundations of Mathematics with Agda. 2019.
  • Rikje, E. Introduction to Homotopy Type Theory. 2019.
• Implementation:
  • Agda-HoTT
  • Agda-premises
  • HoTT-Agda
  • Agda-Base