Theorems · Theorem · algebraic geometry

CategoryTheory.MorphismProperty.grothendieckTopology_eq_toGrothendieck_pretopology

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {P : CategoryTheory.MorphismProperty C}
  [inst_1 : P.IsStableUnderBaseChange] [inst_2 : CategoryTheory.Limits.HasPullbacks C] [inst_3 : P.IsMultiplicative],
  P.grothendieckTopology = P.pretopology.toGrothendieck

If P is also multiplicative, the topology induced by P is the topology induced by the pretopology induced by P.

Defined in

Mathlib.CategoryTheory.Sites.MorphismProperty

Cited by

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Foundations

Depth 40 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsStableUnderBaseChangeCategoryTheory.Limits.HasPullbacksCategoryTheory.MorphismProperty.IsMultiplicative