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[Merged by Bors] - feat(AlgebraicTopology): define the simplicial nerve of a simplicial category #19837

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[Merged by Bors] - feat(AlgebraicTopology): define the simplicial nerve of a simplicial category #19837

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dagurtomas
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@dagurtomas dagurtomas commented Dec 9, 2024 •
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This PR defines the simplicial (/homotopy coherent) nerve of a simplicial category.

Eventually, this will be used to define the infinity-category of anima.

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github-actions bot commented Dec 9, 2024 •
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PR summary 213c7fbc1d

Import changes for modified files

No significant changes to the import graph

Import changes for all files
Files Import difference
Mathlib.AlgebraicTopology.SimplicialNerve (new file) 864

Declarations diff

+ EnrichedFunctor.ext
+ Hom
+ Path
+ Path.le
+ SimplicialNerve
+ SimplicialThickening
+ assoc
+ comp
+ compFunctor
+ comp_app
+ comp_id
+ functor
+ functorMap
+ functor_comp
+ functor_id
+ hom_ext
+ id
+ id_comp
+ instance (J : Type*) [LinearOrder J] :
+ instance (J : Type*) [LinearOrder J] : Category (SimplicialThickening J)
+ instance (J : Type*) [LinearOrder J] : CategoryStruct (SimplicialThickening J)
+ instance (J : Type*) [LinearOrder J] : LinearOrder (SimplicialThickening J)
+ instance {J : Type*} [LinearOrder J] (i j : J) : Category (Path i j)
+ instance {J : Type*} [LinearOrder J] (i j : SimplicialThickening J) : Category (i ⟶ j)
+ nerveEquiv
+ nerveMap
+ orderHom
+ uliftMap

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 relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
  • The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).

@dagurtomas dagurtomas added t-category-theory Category theory t-topology Topological spaces, uniform spaces, metric spaces, filters labels Dec 9, 2024
jcommelin
jcommelin reviewed Dec 11, 2024
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Mathlib/AlgebraicTopology/SimplicialSet/Basic.lean Outdated
Comment on lines 64 to 66
-- Even though `NatTrans.comp_app` is a `@[simp]` lemma, `simp` is unable to prove this.
-- Why is this?
-- Do we want `SSet.comp_app` as a global `@[simp]` lemma?
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Can simp prove this if you pass it SSet.comp_app?

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This is SSet.comp_app. My question was meant as "do we want this as a simp lemma?".

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🤦 -- sorry for reviewing while my mind was foggy

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Anyways, simp does not realize that f and g are natural transformations, because that fact is hidden behind one layer of definitions. So I agree that it would be good to make this lemma a simp-lemma.

jcommelin
jcommelin reviewed Dec 12, 2024
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LGTM, modulo the simp question.

bors d+

Mathlib/AlgebraicTopology/SimplicialSet/Basic.lean Outdated
Comment on lines 64 to 66
-- Even though `NatTrans.comp_app` is a `@[simp]` lemma, `simp` is unable to prove this.
-- Why is this?
-- Do we want `SSet.comp_app` as a global `@[simp]` lemma?
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Anyways, simp does not realize that f and g are natural transformations, because that fact is hidden behind one layer of definitions. So I agree that it would be good to make this lemma a simp-lemma.

Mathlib/AlgebraicTopology/SimplicialNerve.lean Outdated

-- This is to improve automation throughout this file, because `simp` doesn't apply
-- `NatTrans.comp_app` to morphisms of simplicial sets.
attribute [local simp] SSet.comp_app
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As discussed in the other thread, I think we can make it a global simp lemma

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mathlib-bors bot commented Dec 12, 2024

✌️ dagurtomas can now approve this pull request. To approve and merge a pull request, simply reply with bors r+. More detailed instructions are available here.

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bors merge

mathlib-bors bot pushed a commit that referenced this pull request Dec 12, 2024
@dagurtomas
feat(AlgebraicTopology): define the simplicial nerve of a simplicial …
415efa6 
…category (#19837)

This PR defines the simplicial (/homotopy coherent) nerve of a simplicial category.
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mathlib-bors bot commented Dec 12, 2024

Pull request successfully merged into master.

Build succeeded:

@mathlib-bors mathlib-bors bot changed the title feat(AlgebraicTopology): define the simplicial nerve of a simplicial category [Merged by Bors] - feat(AlgebraicTopology): define the simplicial nerve of a simplicial category Dec 12, 2024
@mathlib-bors mathlib-bors bot closed this Dec 12, 2024
@mathlib-bors mathlib-bors bot deleted the dagur/SimplicialNerve branch December 12, 2024 12:14
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