feat(CategoryTheory/Sites): descent data when we have pullbacks

[joelriou]

In this file, given a pseudofunctor F from LocallyDiscrete Cᵒᵖ to Cat, a family of maps f i : X i ⟶ S in the category C, chosen pullbacks sq and threefold wide pullbacks sq₃ for these morphisms, we define a category F.DescentData' sq sq₃ of objects over the X i equipped with a descent data relative to the morphisms f i : X i ⟶ S, where the data and compatibilities are expressed using the chosen pullbacks.

Co-authored-by: Christian Merten

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• depends on: feat(CategoryTheory/Limits): chosen pullbacks #35393

[github-actions]

PR summary 99884c2730

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Limits.Shapes.Pullback.ChosenPullback (new file)	601
Mathlib.CategoryTheory.Sites.Descent.DescentDataPrime (new file)	1063

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Declarations diff

+ ChosenPullback
+ ChosenPullback₃
+ DescentData'
+ Diagonal
+ Hom
+ LiftStruct
+ comm
+ comp_hom
+ comp_pullHom'
+ comp_pullHom''
+ exists_lift
+ hp₂
+ id_hom
+ instance (D : F.DescentData' sq sq₃)
+ instance (D : F.DescentData' sq sq₃) (i₁ i₂ : ι) :
+ instance : Category (F.DescentData' sq sq₃)
+ instance : Nonempty h.Diagonal := by apply LiftStruct.nonempty <;> cat_disch
+ instance : Subsingleton (h.LiftStruct g₁ g₂ b)
+ isPullback
+ isPullback₁
+ isPullback₂
+ isPullback₃
+ isoMk
+ mk'
+ nonempty
+ pullHom'
+ pullHom'_eq_hom
+ pullHom'_eq_pullHom
+ pullHom'_p₁_p₂
+ pullHom'_self
+ pullHom'_self'
+ pullHom'₁₂_eq_pullHom_of_chosenPullback₃
+ pullHom'₁₃_eq_pullHom_of_chosenPullback₃
+ pullHom'₂₃_eq_pullHom_of_chosenPullback₃
+ pullback
+ p₁₂
+ p₁₂_eq_lift
+ p₁₂_p
+ p₁₂_p₁
+ p₁₂_p₂
+ p₁₃
+ p₁₃_eq_lift
+ p₁₃_p
+ p₁₃_p₁
+ p₁₃_p₃
+ p₂
+ p₂₃
+ p₂₃_eq_lift
+ p₂₃_p
+ p₂₃_p₂
+ p₂₃_p₃
+ w
+ w₁
+ w₂
+ w₃
++ hom_ext

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 scripts/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).

[mathlib-dependent-issues]

This PR/issue depends on:

• feat(CategoryTheory/Limits): chosen pullbacks #35393
  By Dependent Issues (🤖). Happy coding!