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feat(higher): add aligned hammock path category - #127

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miuchan merged 1 commit into
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codex/aligned-hammock-path-category
Aug 22, 2026
Merged

feat(higher): add aligned hammock path category#127
miuchan merged 1 commit into
mainfrom
codex/aligned-hammock-path-category

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@miuchan miuchan commented Aug 22, 2026

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Summary

  • add a non-groupoidal generated hammock-path syntax combining executable refinements, arbitrary aligned raw 2-cells, and vertical composition
  • quotient paths by exact presented 2-cell semantics and prove the semantic functor faithful and object-essentially-surjective
  • embed refinement-only paths faithfully, with strict semantic and nerve factorizations
  • give every source 2-cell a canonical one-column representative and prove its right-unitor-conjugated quotient formula
  • expose exact cost-exact nerve actions for refinement, aligned, and source 2-cell edges
  • audit the new declarations and synchronize research boundaries and four-language status docs

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

This PR covers arbitrary aligned cells and every source 2-cell in canonical one-column form. It does not yet normalize every presented quotient 2-cell into alternating aligned/refinement paths, so fullness into the complete linear mapping category, 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 06:06
@miuchan
miuchan merged commit 8861228 into main Aug 22, 2026
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