Theorems · Theorem · category theory

CategoryTheory.Precoverage.toCoverage_le_toCoverage

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {J : CategoryTheory.Precoverage C}
  [inst_1 : J.HasPullbacks] [inst_2 : J.IsStableUnderBaseChange] (K : CategoryTheory.GrothendieckTopology C),
  (J.toCoverage ≤ K.toCoverage) = ∀ ⦃X : C⦄, ∀ S ∈ J.coverings X, CategoryTheory.Sieve.generate S ∈ K X

Defined in

Mathlib.CategoryTheory.Sites.Coverage

Cited by

0 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Precoverage.HasPullbacksCategoryTheory.Precoverage.IsStableUnderBaseChange