├── .Notes (outdated) ├── HowNameSpacesWorkInLean.lean ├── natural_model_univ │ ├── .gitignore │ ├── groupoid_model.tex │ ├── main.pdf │ ├── main.tex │ ├── prooftree.tex │ └── refs.bib └── natural_model_univ_July18.pdf ├── .github └── workflows │ ├── blueprint.yml │ ├── push.yml │ └── push_pr.yml ├── .gitignore ├── .vscode └── settings.json ├── HoTTLean.lean ├── HoTTLean ├── ForMathlib.lean ├── ForMathlib │ ├── CategoryTheory │ │ ├── Bicategory │ │ │ └── Grothendieck.lean │ │ ├── Core.lean │ │ ├── FreeGroupoid.lean │ │ ├── Functor │ │ │ ├── IsPullback.lean │ │ │ └── Iso.lean │ │ ├── Groupoid.lean │ │ ├── Grpd.lean │ │ ├── Localization │ │ │ └── Predicate.lean │ │ ├── MorphismProperty │ │ │ ├── Basic.lean │ │ │ └── WideSubcategory.lean │ │ ├── NatTrans.lean │ │ ├── RepPullbackCone.lean │ │ ├── WeakPullback.lean │ │ ├── Whiskering.lean │ │ └── Yoneda.lean │ └── Tactic │ │ └── CategoryTheory │ │ └── FunctorMap.lean ├── ForPoly.lean ├── Frontend │ ├── Checked.lean │ ├── Commands.lean │ ├── EnvExt.lean │ └── Translation.lean ├── Grothendieck │ ├── Groupoidal │ │ ├── Basic.lean │ │ └── IsPullback.lean │ └── IsPullback.lean ├── Groupoids │ ├── Basic.lean │ ├── ClovenIsofibration.lean │ ├── Id.lean │ ├── IsPullback.lean │ ├── Pi.lean │ ├── Sigma.lean │ ├── UHom.lean │ └── UnstructuredModel.lean ├── Model │ ├── Natural │ │ ├── Interpretation.lean │ │ ├── NaturalModel.lean │ │ └── UHom.lean │ └── Unstructured │ │ ├── Hurewicz.lean │ │ ├── Interpretation.lean │ │ ├── UHom.lean │ │ └── UnstructuredUniverse.lean ├── Pointed │ ├── Basic.lean │ └── IsPullback.lean ├── Prelude.lean ├── Syntax │ ├── Autosubst.lean │ ├── Axioms.lean │ ├── Basic.lean │ ├── EqCtx.lean │ ├── GCongr.lean │ ├── Injectivity.lean │ ├── Inversion.lean │ ├── InversionLemmas.lean │ ├── Substitution.lean │ ├── Synth.lean │ └── Typing.lean ├── Tactic │ ├── GrindCases.lean │ └── MutualInduction.lean └── Typechecker │ ├── Cache.lean │ ├── Equate.lean │ ├── Evaluate.lean │ ├── Synth.lean │ ├── Util.lean │ ├── Value.lean │ └── ValueInversion.lean ├── LICENSE ├── README.md ├── attic ├── Display.lean ├── FibrationForMathlib │ ├── Data │ │ └── Fiber.lean │ ├── Displayed │ │ ├── Basic.lean │ │ ├── Cartesian.lean │ │ ├── Chevalley.lean │ │ ├── Fiber.lean │ │ ├── Fibration.lean │ │ └── widget_test.lean │ └── FibredCats │ │ ├── Basic.lean │ │ ├── CartLift.lean │ │ ├── CartesianLift.lean │ │ ├── Display_test.lean │ │ ├── Displayed_BiCat.lean │ │ ├── Fibration.lean │ │ ├── Total.lean │ │ ├── VerticalLift.lean │ │ └── gaplift_cast.lean ├── ForMathlib.lean ├── ForMathlib │ └── GrothendieckEquiv.lean ├── Groupoids-NaturalModel │ ├── Basic.lean │ ├── Id.lean │ ├── IsPullback.lean │ ├── NaturalModelBase.lean │ ├── Pi.lean │ └── Sigma.lean ├── NaturalModel.lean ├── NaturalModelBase.lean ├── PullbackProofs.lean ├── README.md ├── Russell_PER_MS │ └── NaturalModelPi.lean ├── Syntax │ └── Autosubst.lean ├── Tarski │ ├── NaturalModel.lean │ ├── TarskiNaturalModel.lean │ └── TypeTheory.lean └── Typechecker │ └── SubstList.lean ├── bench ├── measure.lean ├── plot.ipynb └── samplers │ ├── fn.lean │ ├── id.lean │ ├── pair.lean │ └── prod.lean ├── blueprint └── src │ ├── Packages │ └── bussproofs.py │ ├── Templates │ └── prooftree.jinja2 │ ├── blueprint.sty │ ├── chapter │ ├── all.tex │ ├── groupoid_model.tex │ ├── interpretation.tex │ ├── natural_model.tex │ ├── polynomial.tex │ └── syntax.tex │ ├── extra_styles.css │ ├── latexmkrc │ ├── macros │ ├── common.tex │ ├── print.tex │ └── web.tex │ ├── plastex.cfg │ ├── print.tex │ ├── refs.bib │ └── web.tex ├── flake.lock ├── flake.nix ├── home_page ├── 404.html ├── Gemfile ├── Gemfile.lock ├── _config.yml ├── _include │ └── mathjax.html ├── _layouts │ └── default.html ├── _site │ ├── 404.html │ ├── assets │ │ └── css │ │ │ └── style.css │ └── index.html ├── assets │ └── css │ │ └── style.scss └── index.md ├── lake-manifest.json ├── lakefile.lean ├── lean-toolchain ├── scripts └── update_mathlib.sh ├── test.lean └── test ├── basic.lean ├── hott0.lean 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