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Theorems · Theorem · algebraic geometry

AlgebraicGeometry.Scheme.smallGrothendieckTopology_eq_toGrothendieck_smallPretopology

∀ {P Q : CategoryTheory.MorphismProperty AlgebraicGeometry.Scheme} (S : AlgebraicGeometry.Scheme)
  [inst : P.IsStableUnderBaseChange] [inst_1 : P.IsMultiplicative] [inst_2 : P.RespectsIso]
  [inst_3 : Q.IsStableUnderComposition] [inst_4 : Q.IsStableUnderBaseChange] [inst_5 : Q.HasOfPostcompProperty Q],
  P ≤ Q →
    AlgebraicGeometry.Scheme.smallGrothendieckTopology P S =
      (AlgebraicGeometry.Scheme.smallPretopology P Q).toGrothendieck
Defined in
Mathlib.AlgebraicGeometry.Sites.Small
Cited by
2 results in Mathlib
Foundations
Depth 202 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.RespectsIsoCategoryTheory.MorphismProperty.IsStableUnderCompositionCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.MorphismProperty.HasOfPostcompProperty
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AlgebraicGeometry.Scheme.mem_smallGrothendieckTopology · cited by 1Scheme.mem_smallGrothendi…AlgebraicGeometry.Scheme.smallGrothendieckTopologyOfLE_eq_toGrothendieck_smallPretopology · cited by 0Scheme.smallGrothendieckT…Quiver.Hom · cited by 32603Quiver.HomCategoryTheory.Functor.obj · cited by 19642Functor.objTop.top · cited by 9680Top.topCategoryTheory.Functor.map · cited by 8698Functor.mapCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Functor.id · cited by 3333Functor.idAlgebraicGeometry.Scheme · cited by 2540AlgebraicGeometry.SchemeCategoryTheory.Discrete · cited by 2447CategoryTheory.DiscreteSet.ext · cited by 2266Set.extCategoryTheory.MorphismProperty · cited by 2179CategoryTheory.MorphismPr…CategoryTheory.GrothendieckTopology · cited by 1415CategoryTheory.Grothendie…CategoryTheory.Limits.WalkingPair · cited by 1319Limits.WalkingPairCategoryTheory.Over · cited by 935CategoryTheory.OverCategoryTheory.Comma.left · cited by 886Comma.leftCategoryTheory.Functor.fromPUnit · cited by 769Functor.fromPUnitScheme.smallGrothendieckTopol…CITED BYCITES

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