Theorems · Theorem · category theory

CategoryTheory.Pretopology.mem_toGrothendieck

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasPullbacks C]
  (K : CategoryTheory.Pretopology C) (X : C) (S : CategoryTheory.Sieve X),
  S ∈ K.toGrothendieck X ↔ ∃ R ∈ K.coverings X, R ≤ S.arrows

Defined in

Mathlib.CategoryTheory.Sites.Pretopology

Cited by

2 results in Mathlib

Foundations

Depth 33 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasPullbacks