Theorems · Theorem · category theory

CategoryTheory.MorphismProperty.relative.property

∀ {C : Type u₁} [inst : CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [inst_1 : CategoryTheory.Category.{v₂, u₂} D]
  {F : CategoryTheory.Functor C D} {X Y : D} {P : CategoryTheory.MorphismProperty C} {f : X ⟶ Y},
  CategoryTheory.MorphismProperty.relative F P f →
    ∀ ⦃a b : C⦄ (g : F.obj a ⟶ Y) (fst : F.obj b ⟶ X) (snd : b ⟶ a),
      CategoryTheory.IsPullback fst (F.map snd) f g → P snd

Defined in

Mathlib.CategoryTheory.MorphismProperty.Representable

Cited by

4 results in Mathlib

Foundations

Depth 6 from the axioms · uses no axioms

Assumes

CategoryTheory.CategoryCategoryTheory.Category