Theorems · Definition · category theory

CategoryTheory.Sheaf.IsLocallySurjective

{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)] →
                [CategoryTheory.ConcreteCategory A FA] → {F₁ F₂ : CategoryTheory.Sheaf J A} → (F₁ ⟶ F₂) → Prop

If φ : F₁ ⟶ F₂ is a morphism of sheaves, this is an abbreviation for Presheaf.IsLocallySurjective J φ.val.

Defined in

Mathlib.CategoryTheory.Sites.LocallySurjective

Cited by

11 results in Mathlib

Foundations

Depth 35 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategory