Two-Level Type Theory
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types
.gitignore
.project
Makefile
README.md
facts.lean
fibrant.lean
fibrantlimits.lean
finite.lean
inverse.lean
limit.lean
matching.lean
pullbacks.lean
release.sh
simplicial.lean

README.md

Lean Formalisation of Two-Level Type Theory

Requires Lean 2 (version 0.2.0) to compile.

Contents

File
fibrant.lean implementation of the two-level type theory
fibrantlimits.lean proof of Theorem 15 (every Reedy fibrant diagram has a fibrant limit)
finite.lean facts about finite sets and categories
inverse.lean definition of inverse categories
limit.lean definition of limits and construction of limits in category of pretypes.
matching.lean definition of the matching object
pullbacks.lean definition of a pullback, constructed explicitly and using the limit of a diagram along with a proof these definitions are equivalent. Proof of the Lemma 7 (pullback of a fibration along f is a fibration)
simplicial.lean initial definition of semi-simplicial types (work in progress)
facts.lean some auxiliary lemmas which we could not find in the standard library

Compilation

Use make to compile the project, or run linja directly.