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feat(higher): characterize refinement semantic image - #126

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miuchan merged 1 commit into
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codex/hammock-refinement-image-groupoid
Aug 22, 2026
Merged

feat(higher): characterize refinement semantic image#126
miuchan merged 1 commit into
mainfrom
codex/hammock-refinement-image-groupoid

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@miuchan miuchan commented Aug 22, 2026

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Summary

  • define the exact refinement-generated quotient-2-cell image as a subgroupoid of the linear hammock mapping category
  • prove semantic refinement paths are full, faithful, essentially surjective, and categorically equivalent onto that image
  • lift the equivalence to a nerve equivalence with an explicit simplicial homotopy inverse and strict semantic factorization
  • audit the new flagship declarations and synchronize the blueprint, conjecture boundary, model matrix, and four-language status docs

Verification

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

Boundary

This PR characterizes the exact image of executable refinements. It does not prove that this image covers every quotient 2-cell required by a standard derived/hammock mapping-space model; critical-pair coherence, reduced-hammock invariance, 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 05:35
@miuchan
miuchan merged commit fd7e191 into main Aug 22, 2026
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