Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.transitive

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] {X : C} {S : CategoryTheory.Sieve X}
  (J : CategoryTheory.GrothendieckTopology C),
  S ∈ J X →
    ∀ (R : CategoryTheory.Sieve X),
      (∀ ⦃Y : C⦄ ⦃f : Y ⟶ X⦄, S.arrows f → CategoryTheory.Sieve.pullback f R ∈ J Y) → R ∈ J X

Defined in

Mathlib.CategoryTheory.Sites.Grothendieck

Cited by

16 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.Category