Theorems · Theorem · category theory

CategoryTheory.Presieve.mem_comap_jointlySurjectivePrecoverage_iff

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] (F : CategoryTheory.Functor C (Type u)) {X : C}
  {R : CategoryTheory.Presieve X},
  R ∈ (CategoryTheory.Precoverage.comap F CategoryTheory.Types.jointlySurjectivePrecoverage).coverings X ↔
    ∀ (x : F.obj X), ∃ Y f, R f ∧ x ∈ Set.range ⇑(CategoryTheory.ConcreteCategory.hom (F.map f))

Defined in

Mathlib.CategoryTheory.Sites.JointlySurjective

Cited by

0 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

CategoryTheory.Category