Theorems · Theorem · category theory

CategoryTheory.Precoverage.mem_toGrothendieck_iff_of_isStableUnderComposition

∀ {C : Type u_2} [inst : CategoryTheory.Category.{u_1, u_2} C] {J : CategoryTheory.Precoverage C}
  [J.IsStableUnderComposition] [J.IsStableUnderBaseChange] [J.HasPullbacks] [J.HasIsos] {X : C}
  {S : CategoryTheory.Sieve X}, S ∈ J.toGrothendieck X ↔ ∃ R ∈ J.coverings X, R ≤ S.arrows

Defined in

Mathlib.CategoryTheory.Sites.PrecoverageToGrothendieck

Cited by

3 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Precoverage.IsStableUnderCompositionCategoryTheory.Precoverage.IsStableUnderBaseChangeCategoryTheory.Precoverage.HasPullbacksCategoryTheory.Precoverage.HasIsos