[Merged by Bors] - feat(AlgebraicTopology): StrictSegal simplicial sets are quasicategories #19270
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PR summary 321de16000
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| File | Base Count | Head Count | Change |
|---|---|---|---|
| Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal | 821 | 823 | +2 (+0.24%) |
Import changes for all files
| Files | Import difference |
|---|---|
Mathlib.AlgebraicTopology.SimplicialSet.StrictSegal |
2 |
Declarations diff
+ Path.map
+ horn.spineId
+ horn.spineId_map_hornInclusion
+ id
+ id_eq_objEquiv_symm
+ instance : Quasicategory (nerve C) := inferInstance
+ instance : Quasicategory X := by
+ map_interval
+ mkOfSucc_δ_eq
+ mkOfSucc_δ_gt
+ mkOfSucc_δ_lt
+ objEquiv_id
+ spineToSimplex_map
+ spine_δ_arrow_eq
+ spine_δ_arrow_gt
+ spine_δ_arrow_lt
+ spine_δ_vertex_ge
+ spine_δ_vertex_lt
+ standardSimplex.spineId
You can run this locally as follows
## summary with just the declaration names:
./scripts/declarations_diff.sh <optional_commit>
## more verbose report:
./scripts/declarations_diff.sh long <optional_commit>The doc-module for script/declarations_diff.sh contains some details about this script.
No changes to technical debt.
You can run this locally as
./scripts/technical-debt-metrics.sh pr_summary
- The
relativevalue is the weighted sum of the differences with weight given by the inverse of the current value of the statistic. - The
absolutevalue is therelativevalue divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).
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Thank you for the careful review @joelriou @jcommelin. bors merge |
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…ies (#19270) We prove that any simplicial set satisfying the `StrictSegal` condition introduced in #18499 is a quasicategory. This implies that the nerve of a category is a quasicategory. We construct a solution to the lifting problem against `hornInclusion n i` as a `spineToSimplex` of the path in the image of the spine of the standard simplex. To prove that this extension restricts to the appropriate map on the horn, we apply `spineInjective`, reducing the question of equality between two `n`-simplices in `X` to that of equality between the paths along their spines. The remainder of the proof is a straightforward application of basic properties relating spines of simplices to their faces. Co-Authored-By: [Johan Commelin](https://github.com/jcommelin) and [Emily Riehl](https://github.com/emilyriehl)
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We add the file `Mathlib/AlgebraicTopology/Quasicategory/StrictSegal.lean` and move the proof (implemented in #19270) that any `StrictSegal` simplicial set is a `Quasicategory`.
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We add the file `Mathlib/AlgebraicTopology/Quasicategory/Nerve.lean` and move the proof (implemented in #19270) that the nerve of a category is a `Quasicategory`.
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We prove that any simplicial set satisfying the
StrictSegalcondition introduced in #18499 is a quasicategory. This implies that the nerve of a category is a quasicategory.We construct a solution to the lifting problem against
hornInclusion n ias aspineToSimplexof the path in the image of the spine of the standard simplex.To prove that this extension restricts to the appropriate map on the horn, we apply
spineInjective, reducing the question of equality between twon-simplices inXto that of equality between the paths along their spines. The remainder of the proof is a straightforward application of basic properties relating spines of simplices to their faces.Co-Authored-By: Johan Commelin and Emily Riehl