Theorems · Theorem · category theory

CategoryTheory.Functor.relativelyRepresentable.isPullback

∀ {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} {f : X ⟶ Y} (hf : F.relativelyRepresentable f) {a : C} (g : F.obj a ⟶ Y),
  CategoryTheory.IsPullback (hf.fst g) (F.map (hf.snd g)) f g

Defined in

Mathlib.CategoryTheory.MorphismProperty.Representable

Cited by

7 results in Mathlib

Foundations

Depth 13 from the axioms · uses Classical.choice

Assumes

CategoryTheory.CategoryCategoryTheory.Category