Skip to content

feat(higher): prove hammock normalization naturality - #129

Merged
miuchan merged 1 commit into
mainfrom
codex/hammock-normalization-naturality
Aug 22, 2026
Merged

feat(higher): prove hammock normalization naturality#129
miuchan merged 1 commit into
mainfrom
codex/hammock-normalization-naturality

Conversation

@miuchan

@miuchan miuchan commented Aug 22, 2026

Copy link
Copy Markdown
Owner

Summary

  • expose exact atom, empty, and binary-append equations for linear normalization
  • prove append-isomorphism naturality around arbitrary left- and right-whiskered quotient 2-cells by exchange and cancellation
  • prove normalized semantics commutes with raw left and right whiskering
  • normalize raw source-identity and inverse generators using unitor equality, and prove equality transport preserves normalizability
  • close the identity, original, source-identity, vertical-composition, both-whiskering, and transport induction branches
  • define StructuralGeneratorNormalizable with exactly twelve remaining structural obligations and prove it implies normalization of every raw cell
  • expose a cost-exact machine-facing normalization core and synchronize audits and four-language boundaries

Verification

  • lake build Ript.ForMathlib.CategoryTheory.Bicategory.MarkedZigzagAlignedHammock
  • lake build Ript.Higher.CostExactZigzagMappingSpace
  • lake build Ript.Audit.Lint
  • ./scripts/check-axioms.sh
  • ./scripts/quality-gate.sh

Boundary

The all-cell induction theorem is conditional on twelve explicit, still-unproved structural generator fields: source composition and inverse, marked unit/counit and inverses, associator and inverse, and left/right unitors and inverses. No unconditional fullness or complete normalization claim is made. Semantic fullness, critical-pair coherence, reduced-hammock invariance, standard weak-equivalence packaging, and the final Dwyer--Kan/Rezk theorem remain open.

@miuchan
miuchan marked this pull request as ready for review August 22, 2026 07:46
@miuchan
miuchan merged commit c547f37 into main Aug 22, 2026
1 check passed
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment

Labels

None yet

Projects

None yet

Development

Successfully merging this pull request may close these issues.

1 participant