feat(CategoryTheory): Guitart exact squares and "base change" for Kan extensions

[joelriou]

Given a Guitart exact square w : T ⋙ R ⟶ L ⋙ B, we show that under suitable assumptions, the base change morphism (whiskeringLeft C₁ C₂ D).obj T ⋙ L.lan ⟶ R.lan ⋙ (whiskeringLeft C₃ C₄ D).obj B is an isomorphism.

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• depends on: feat(CategoryTheory): Guitart exact squares and Kan extensions #30382

[github-actions]

PR summary cc0d5cbbe4

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.GuitartExact.KanExtension (new file)	640

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Declarations diff

+ IsPointwiseLeftKanExtension.compTwoSquare
+ compTwoSquare
+ hasColimit_comp_iff
+ hasLeftKanExtension
+ hasLimit_comp_iff
+ hasPointwiseLeftKanExtension
+ hasPointwiseLeftKanExtensionAt_iff
+ hasPointwiseLeftKanExtension_iff
+ instance (Y : D) : Subsingleton (E.IsPointwiseLeftKanExtensionAt Y)
+ instance (Y : D) : Subsingleton (E.IsPointwiseRightKanExtensionAt Y)
+ instance [∀ (F : C₁ ⥤ D), L.HasLeftKanExtension F]
+ isIso_lanAdjunction_homEquiv_symm_iff
+ isIso_lanBaseChange_app
+ isIso_lanBaseChange_app_iff
+ isIso_ranAdjunction_homEquiv_iff
+ isPointwiseLeftKanExtensionAtCompTwoSquareEquiv
+ isPointwiseLeftKanExtensionEquivOfGuitartExact
+ isPointwiseLeftKanExtensionOfCompTwoSquare
+ lanBaseChange
+ nonempty_isPointwiseLeftKanExtensionAt_compTwoSquare_iff

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.

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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).

[mathlib4-dependent-issues-bot]

This PR/issue depends on:

• feat(CategoryTheory): Guitart exact squares and Kan extensions #30382
  By Dependent Issues (🤖). Happy coding!