feat(CategoryTheory/Sites): add the Grothendieck topology generated by a precoverage

[BGuillemet]

Add the file PrecoverageToGrothendieck.lean, in which the Grothendieck topology generated by a precoverage is defined as Precoverage.toGrothendieck. This replace the previous Precoverage.toGrothendieck, which was defined only in the case of a precoverage having pullbacks and being stable under base change. The equivalence between the two constructions is Precoverage.toGrothendieck_toCoverage.

Prove Precoverage.isSheaf_toGrothendieck_iff: given a precoverage J, a type-valued presheaf is a sheaf for J.toGrothendieck if and only if it is a sheaf for all the pullback sieves of the presieves in J. The proof is based on the previous proof of isSheaf_coverage, which is now a consequence of Precoverage.isSheaf_toGrothendieck_iff.

---

[github-actions]

PR summary 43dc3a9ad0

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference
186 files Mathlib.Algebra.Category.ModuleCat.Sheaf.Generators Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackContinuous Mathlib.Algebra.Category.ModuleCat.Sheaf.PullbackFree Mathlib.Algebra.Category.ModuleCat.Sheaf.PushforwardContinuous Mathlib.Algebra.Category.ModuleCat.Sheaf.Quasicoherent Mathlib.AlgebraicGeometry.AffineScheme Mathlib.AlgebraicGeometry.AffineSpace Mathlib.AlgebraicGeometry.AffineTransitionLimit Mathlib.AlgebraicGeometry.Cover.Directed Mathlib.AlgebraicGeometry.Cover.MorphismProperty Mathlib.AlgebraicGeometry.Cover.Open Mathlib.AlgebraicGeometry.Cover.Over Mathlib.AlgebraicGeometry.Cover.Sigma Mathlib.AlgebraicGeometry.Fiber Mathlib.AlgebraicGeometry.FunctionField Mathlib.AlgebraicGeometry.GammaSpecAdjunction Mathlib.AlgebraicGeometry.GluingOneHypercover Mathlib.AlgebraicGeometry.Gluing Mathlib.AlgebraicGeometry.IdealSheaf.Basic Mathlib.AlgebraicGeometry.IdealSheaf.Functorial Mathlib.AlgebraicGeometry.IdealSheaf.Subscheme Mathlib.AlgebraicGeometry.IdealSheaf Mathlib.AlgebraicGeometry.LimitsOver Mathlib.AlgebraicGeometry.Limits Mathlib.AlgebraicGeometry.Modules.Presheaf Mathlib.AlgebraicGeometry.Modules.Sheaf Mathlib.AlgebraicGeometry.Modules.Tilde Mathlib.AlgebraicGeometry.Morphisms.AffineAnd Mathlib.AlgebraicGeometry.Morphisms.Affine Mathlib.AlgebraicGeometry.Morphisms.Basic Mathlib.AlgebraicGeometry.Morphisms.ClosedImmersion Mathlib.AlgebraicGeometry.Morphisms.Constructors Mathlib.AlgebraicGeometry.Morphisms.Descent Mathlib.AlgebraicGeometry.Morphisms.Etale Mathlib.AlgebraicGeometry.Morphisms.FinitePresentation Mathlib.AlgebraicGeometry.Morphisms.FiniteType Mathlib.AlgebraicGeometry.Morphisms.Finite Mathlib.AlgebraicGeometry.Morphisms.Flat Mathlib.AlgebraicGeometry.Morphisms.FormallyUnramified Mathlib.AlgebraicGeometry.Morphisms.Immersion Mathlib.AlgebraicGeometry.Morphisms.Integral Mathlib.AlgebraicGeometry.Morphisms.IsIso Mathlib.AlgebraicGeometry.Morphisms.LocalClosure Mathlib.AlgebraicGeometry.Morphisms.LocalIso Mathlib.AlgebraicGeometry.Morphisms.OpenImmersion Mathlib.AlgebraicGeometry.Morphisms.Preimmersion Mathlib.AlgebraicGeometry.Morphisms.Proper Mathlib.AlgebraicGeometry.Morphisms.QuasiCompact Mathlib.AlgebraicGeometry.Morphisms.QuasiSeparated Mathlib.AlgebraicGeometry.Morphisms.RingHomProperties Mathlib.AlgebraicGeometry.Morphisms.Separated Mathlib.AlgebraicGeometry.Morphisms.Smooth Mathlib.AlgebraicGeometry.Morphisms.SurjectiveOnStalks Mathlib.AlgebraicGeometry.Morphisms.UnderlyingMap Mathlib.AlgebraicGeometry.Morphisms.UniversallyClosed Mathlib.AlgebraicGeometry.Morphisms.UniversallyInjective Mathlib.AlgebraicGeometry.Morphisms.UniversallyOpen Mathlib.AlgebraicGeometry.Noetherian Mathlib.AlgebraicGeometry.OpenImmersion Mathlib.AlgebraicGeometry.Over Mathlib.AlgebraicGeometry.PointsPi Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Basic Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Proper Mathlib.AlgebraicGeometry.ProjectiveSpectrum.Scheme Mathlib.AlgebraicGeometry.ProjectiveSpectrum.StructureSheaf Mathlib.AlgebraicGeometry.Properties Mathlib.AlgebraicGeometry.PullbackCarrier Mathlib.AlgebraicGeometry.Pullbacks Mathlib.AlgebraicGeometry.QuasiAffine Mathlib.AlgebraicGeometry.RationalMap Mathlib.AlgebraicGeometry.ResidueField Mathlib.AlgebraicGeometry.Restrict Mathlib.AlgebraicGeometry.Scheme Mathlib.AlgebraicGeometry.Sites.BigZariski Mathlib.AlgebraicGeometry.Sites.Etale Mathlib.AlgebraicGeometry.Sites.MorphismProperty Mathlib.AlgebraicGeometry.Sites.Pretopology Mathlib.AlgebraicGeometry.Sites.Representability Mathlib.AlgebraicGeometry.Sites.SmallAffineZariski Mathlib.AlgebraicGeometry.Sites.Small Mathlib.AlgebraicGeometry.Spec Mathlib.AlgebraicGeometry.SpreadingOut Mathlib.AlgebraicGeometry.Stalk Mathlib.AlgebraicGeometry.StructureSheaf Mathlib.AlgebraicGeometry.ValuativeCriterion Mathlib.CategoryTheory.Abelian.GrothendieckAxioms.Sheaf Mathlib.CategoryTheory.Sites.Coherent.Basic Mathlib.CategoryTheory.Sites.Coherent.CoherentSheaves Mathlib.CategoryTheory.Sites.Coherent.CoherentTopology Mathlib.CategoryTheory.Sites.Coherent.Comparison Mathlib.CategoryTheory.Sites.Coherent.Equivalence Mathlib.CategoryTheory.Sites.Coherent.ExtensiveColimits Mathlib.CategoryTheory.Sites.Coherent.ExtensiveSheaves Mathlib.CategoryTheory.Sites.Coherent.ExtensiveTopology Mathlib.CategoryTheory.Sites.Coherent.LocallySurjective Mathlib.CategoryTheory.Sites.Coherent.ReflectsPrecoherent Mathlib.CategoryTheory.Sites.Coherent.ReflectsPreregular Mathlib.CategoryTheory.Sites.Coherent.RegularSheaves Mathlib.CategoryTheory.Sites.Coherent.RegularTopology Mathlib.CategoryTheory.Sites.Coherent.SequentialLimit Mathlib.CategoryTheory.Sites.Coherent.SheafComparison Mathlib.CategoryTheory.Sites.ConstantSheaf Mathlib.CategoryTheory.Sites.Continuous Mathlib.CategoryTheory.Sites.CoverLifting Mathlib.CategoryTheory.Sites.CoverPreserving Mathlib.CategoryTheory.Sites.Coverage Mathlib.CategoryTheory.Sites.DenseSubsite.Basic Mathlib.CategoryTheory.Sites.DenseSubsite.InducedTopology Mathlib.CategoryTheory.Sites.DenseSubsite.SheafEquiv Mathlib.CategoryTheory.Sites.Descent.DescentData Mathlib.CategoryTheory.Sites.Descent.IsPrestack Mathlib.CategoryTheory.Sites.Equivalence Mathlib.CategoryTheory.Sites.GlobalSections Mathlib.CategoryTheory.Sites.Hypercover.Homotopy Mathlib.CategoryTheory.Sites.Hypercover.IsSheaf Mathlib.CategoryTheory.Sites.Hypercover.One Mathlib.CategoryTheory.Sites.Monoidal Mathlib.CategoryTheory.Sites.MorphismProperty Mathlib.CategoryTheory.Sites.Over Mathlib.CategoryTheory.Sites.PreservesLocallyBijective Mathlib.CategoryTheory.Sites.PseudofunctorSheafOver Mathlib.CategoryTheory.Sites.Pullback Mathlib.CategoryTheory.Sites.SheafCohomology.Basic Mathlib.CategoryTheory.Sites.SheafHom Mathlib.Condensed.AB Mathlib.Condensed.Basic Mathlib.Condensed.CartesianClosed Mathlib.Condensed.Discrete.Basic Mathlib.Condensed.Discrete.Characterization Mathlib.Condensed.Discrete.Colimit Mathlib.Condensed.Discrete.LocallyConstant Mathlib.Condensed.Discrete.Module Mathlib.Condensed.Epi Mathlib.Condensed.Equivalence Mathlib.Condensed.Explicit Mathlib.Condensed.Functors Mathlib.Condensed.Light.AB Mathlib.Condensed.Light.Basic Mathlib.Condensed.Light.CartesianClosed Mathlib.Condensed.Light.Epi Mathlib.Condensed.Light.Explicit Mathlib.Condensed.Light.Functors Mathlib.Condensed.Light.Instances Mathlib.Condensed.Light.InternallyProjective Mathlib.Condensed.Light.Limits Mathlib.Condensed.Light.Module Mathlib.Condensed.Light.Monoidal Mathlib.Condensed.Light.Small Mathlib.Condensed.Light.TopCatAdjunction Mathlib.Condensed.Light.TopComparison Mathlib.Condensed.Limits Mathlib.Condensed.Module Mathlib.Condensed.Solid Mathlib.Condensed.TopCatAdjunction Mathlib.Condensed.TopComparison Mathlib.Geometry.Manifold.Sheaf.Basic Mathlib.Geometry.Manifold.Sheaf.LocallyRingedSpace Mathlib.Geometry.Manifold.Sheaf.Smooth Mathlib.Geometry.RingedSpace.Basic Mathlib.Geometry.RingedSpace.LocallyRingedSpace.HasColimits Mathlib.Geometry.RingedSpace.LocallyRingedSpace.ResidueField Mathlib.Geometry.RingedSpace.LocallyRingedSpace Mathlib.Geometry.RingedSpace.OpenImmersion Mathlib.Geometry.RingedSpace.PresheafedSpace.Gluing Mathlib.Geometry.RingedSpace.SheafedSpace Mathlib.Geometry.RingedSpace.Stalks Mathlib.Topology.Category.CompHaus.EffectiveEpi Mathlib.Topology.Category.CompHausLike.EffectiveEpi Mathlib.Topology.Category.LightProfinite.EffectiveEpi Mathlib.Topology.Category.Profinite.EffectiveEpi Mathlib.Topology.Category.Stonean.EffectiveEpi Mathlib.Topology.Sheaves.Alexandrov Mathlib.Topology.Sheaves.CommRingCat Mathlib.Topology.Sheaves.Functors Mathlib.Topology.Sheaves.LocalPredicate Mathlib.Topology.Sheaves.LocallySurjective Mathlib.Topology.Sheaves.PUnit Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts Mathlib.Topology.Sheaves.SheafCondition.OpensLeCover Mathlib.Topology.Sheaves.SheafCondition.PairwiseIntersections Mathlib.Topology.Sheaves.SheafCondition.Sites Mathlib.Topology.Sheaves.SheafCondition.UniqueGluing Mathlib.Topology.Sheaves.SheafOfFunctions Mathlib.Topology.Sheaves.Sheafify Mathlib.Topology.Sheaves.Skyscraper Mathlib.Topology.Sheaves.Stalks	1
Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck (new file)	539

---

Declarations diff

+ Coverage.toGrothendieck_toPrecoverage
+ Precoverage.toCoverage
+ Precoverage.toGrothendieck_toCoverage
+ Saturate
+ Saturate.pullback
+ generate_mem_toGrothendieck
+ isSheaf_toGrothendieck_iff
+ saturate_iff_saturate_toPrecoverage
+ toGrothendieck_eq_sInf
+-+- toGrothendieck
- toCoverage

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).

[chrisflav]

Thanks!
maintainer delegate

[github-actions]

🚀 Pull request has been placed on the maintainer queue by chrisflav.