Theorems · Theorem · category theory

CategoryTheory.Presheaf.isLocallySurjective_presheafToSheaf_map_iff

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] (J : CategoryTheory.GrothendieckTopology C) {A : Type u'}
  [inst_1 : CategoryTheory.Category.{v', u'} A] {FA : A → A → Type u_1} {CA : A → Type w'}
  [inst_2 : (X Y : A) → FunLike (FA X Y) (CA X) (CA Y)] [inst_3 : CategoryTheory.ConcreteCategory A FA]
  [inst_4 : CategoryTheory.HasWeakSheafify J A] [J.WEqualsLocallyBijective A] {P Q : CategoryTheory.Functor Cᵒᵖ A}
  (φ : P ⟶ Q),
  CategoryTheory.Sheaf.IsLocallySurjective ((CategoryTheory.presheafToSheaf J A).map φ) ↔
    CategoryTheory.Presheaf.IsLocallySurjective J φ

Defined in

Mathlib.CategoryTheory.Sites.LocallyBijective

Cited by

1 results in Mathlib

Foundations

Depth 42 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.HasWeakSheafifyCategoryTheory.GrothendieckTopology.WEqualsLocallyBijective