Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.exists_map_eq_of_presieve

∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] {P : CategoryTheory.MorphismProperty C} {S : C}
  [P.IsStableUnderComposition],
  ∀ K ≤ P.precoverage,
    ∀ {X : P.Over ⊤ S} {R : CategoryTheory.Presieve ((CategoryTheory.MorphismProperty.Over.forget P ⊤ S).obj X)},
      R ∈
          (CategoryTheory.Precoverage.comap (CategoryTheory.Over.forget S) K).coverings
            ((CategoryTheory.MorphismProperty.Over.forget P ⊤ S).obj X) →
        ∃ T, CategoryTheory.Presieve.map (CategoryTheory.MorphismProperty.Over.forget P ⊤ S) T = R

Defined in

Mathlib.CategoryTheory.MorphismProperty.CommaSites

Cited by

2 results in Mathlib

Foundations

Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.MorphismProperty.IsStableUnderComposition