feat(CategoryTheory): criterion for `ObjectProperty.ind` in finitely accessible categories

[chrisflav]

We show that if C is finitely accessible and P implies finitely presentable, then X satisfies ind P if and only if every morphism Z ⟶ X from a finitely presentable object factors via an object satisfying W. We also add the analogous statement for morphism properties.

From Proetale.

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• [x] depends on: #33001

[github-actions[bot]]

PR summary 99bc1514ad

Import changes exceeding 2%

%	File
+5.71%	Mathlib.CategoryTheory.MorphismProperty.Ind
+8.08%	Mathlib.CategoryTheory.ObjectProperty.Ind

Import changes for modified files

Dependency changes

File	Base Count	Head Count	Change
Mathlib.CategoryTheory.ObjectProperty.Ind	743	803	+60 (+8.08%)
Mathlib.CategoryTheory.MorphismProperty.Ind	770	814	+44 (+5.71%)
Mathlib.CategoryTheory.Presentable.Dense	798	801	+3 (+0.38%)

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Presentable.Dense	3
Mathlib.CategoryTheory.MorphismProperty.Ind	44
Mathlib.CategoryTheory.ObjectProperty.Ind	60

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Declarations diff

+ IsFinitelyAccessibleCategory + IsLocallyFinitelyPresentable + ObjectProperty.isFinitelyPresentable_eq_isCardinalPresentable + instance (X : (ObjectProperty.isFinitelyPresentable.{w} C).FullSubcategory) : + instance [IsFinitelyAccessibleCategory.{w} C] (X : C) : + of_essentiallySmall_index ++ ind_iff_exists ++ instance [IsFinitelyAccessibleCategory.{w} C] :

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:

• ~~leanprover-community/mathlib4#33001~~ By Dependent Issues (🤖). Happy coding!

[mathlib4-merge-conflict-bot]

This pull request has conflicts, please merge master and resolve them.

[robin-carlier]

Thanks!

maintainer merge

[github-actions[bot]]

🚀 Pull request has been placed on the maintainer queue by robin-carlier.

[joelriou]

Thanks!

bors merge

[mathlib-bors[bot]]

Pull request successfully merged into master.

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