[Merged by Bors] - feat(AlgebraicTopology/SimplexCategory/GeneratorsRelations): the category SimplexCategoryGenRel

[robin-carlier]

Define SimplexCategoryGenRel as the category presented by generators and relation by the following data:

• Objects are natural numbers. The constructor is SimplexCategoryGenRel.mk.
• Morphisms are generated by two classes of morphisms : δ {n : ℕ} (i : Fin (n + 2)) : mk n ⟶ mk (n + 1) and σ {n : ℕ} (i : Fin (n + 1)) : mk (n + 1) ⟶ mk n
• Morphisms are subject to the simplicial relations, i.e the relations proven for SimplexCategory in AlgebraicTopology/SimplexCategory.lean

We provide induction principles for objects and morphisms for this category, and construct a canonical functor to SimplexCategory.

Part of a series of PR formalising that SimplexCategoryGenRel is equivalent to SimplexCategory.

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• depends on: [Merged by Bors] - feat(CategoryTheory/MorphismProperty): multiplicative closure of a MorphismProperty #21864

[github-actions]

PR summary dc4f072efa

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.Basic (new file)	832

---

Declarations diff

+ FreeSimplexQuiver
+ FreeSimplexQuiver.len
+ FreeSimplexQuiver.mk
+ Hom
+ SimplexCategoryGenRel
+ SimplexCategoryGenRel.mk
+ degeneracies
+ ext
+ faces
+ generators
+ homRel
+ hom_induction
+ hom_induction'
+ len
+ mk_len
+ multiplicativeClosure_isGenerator_eq_top
+ quiv
+ rec
+ toSimplexCategory
+ toSimplexCategory_len
+ toSimplexCategory_map_δ
+ toSimplexCategory_map_σ
+ toSimplexCategory_obj_mk
+ δ_comp_δ
+ δ_comp_δ_nat
+ δ_comp_σ_of_gt
+ δ_comp_σ_of_le
+ δ_comp_σ_self
+ δ_comp_σ_succ
+ σ_comp_σ
+ σ_comp_σ_nat
+++ δ
+++ σ

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).

[joelriou]

Apart from some little syntax improvements, this looks good to me!

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• [Merged by Bors] - feat(CategoryTheory/MorphismProperty): multiplicative closure of a MorphismProperty #21864
  By Dependent Issues (🤖). Happy coding!

[joelriou]

Could you merge with master?

[joelriou]

Thanks!

bors merge

[mathlib-bors]

Pull request successfully merged into master.

Build succeeded:

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