Theorems · Theorem · category theory

CategoryTheory.Presheaf.isLocallySurjective_iff_of_fac

∀ {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]
  {F₁ F₂ F₃ : CategoryTheory.Functor Cᵒᵖ A} {f₁ : F₁ ⟶ F₂} {f₂ : F₂ ⟶ F₃} {f₃ : F₁ ⟶ F₃},
  CategoryTheory.CategoryStruct.comp f₁ f₂ = f₃ →
    ∀ [CategoryTheory.Presheaf.IsLocallySurjective J f₁],
      CategoryTheory.Presheaf.IsLocallySurjective J f₃ ↔ CategoryTheory.Presheaf.IsLocallySurjective J f₂

Defined in

Mathlib.CategoryTheory.Sites.LocallySurjective

Cited by

1 results in Mathlib

Foundations

Depth 37 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryFunLikeCategoryTheory.ConcreteCategoryCategoryTheory.Presheaf.IsLocallySurjective