feat(CategoryTheory/Presentable): presentable objects in Type

[joelriou]

In this file, we show that if κ : Cardinal.{u} is a regular cardinal, then X : Type u is κ-presentable in the category of types iff HasCardinalLT X κ holds.

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• depends on: feat(SetTheory): more API for HasCardinalLT #30633

[github-actions]

PR summary 0d837987e5

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
Mathlib.CategoryTheory.Presentable.Type (new file)	867

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Declarations diff

+ IsRegular.lift
+ Set
+ cocone
+ functor
+ hasCardinalLT_iUnion
+ hasCardinalLT_lift_iff
+ hasCardinalLT_of_finite
+ hasCardinalLT_prod
+ hasCardinalLT_prod'
+ hasCardinalLT_sigma
+ hasCardinalLT_sigma'
+ hasCardinalLT_subtype_iSup
+ hasCardinalLT_subtype_max
+ hasCardinalLT_ulift_iff
+ hasCardinalLT_union
+ instance (X : Type u) : IsPresentable.{u} X := by
+ isCardinalPresentable
+ isCardinalPresentable_iff
+ isColimitCocone
+ isFiltered_of_aleph0_le
+ isRegular_lift_iff
+ jointly_surjective_of_isColimit₂
++ instance [Fact κ.IsRegular] :

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(SetTheory): more API for HasCardinalLT #30633
  By Dependent Issues (🤖). Happy coding!