Theorems · Theorem · category theory

CategoryTheory.GrothendieckTopology.W_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (J : CategoryTheory.GrothendieckTopology C)
  {A : Type u_2} [inst_1 : CategoryTheory.Category.{v_2, u_2} A] [inst_2 : CategoryTheory.HasWeakSheafify J A]
  {P₁ P₂ : CategoryTheory.Functor Cᵒᵖ A} (f : P₁ ⟶ P₂),
  J.W f ↔ CategoryTheory.IsIso ((CategoryTheory.presheafToSheaf J A).map f)

Defined in

Mathlib.CategoryTheory.Sites.Localization

Cited by

3 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.HasWeakSheafify