Theorems · Theorem · category theory

CategoryTheory.Functor.relativelyRepresentable.lift_fst

∀ {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}
  {c : C} (i : F.obj c ⟶ X) (h : c ⟶ a)
  (hi : CategoryTheory.CategoryStruct.comp i f = CategoryTheory.CategoryStruct.comp (F.map h) g) [inst_2 : F.Full],
  CategoryTheory.CategoryStruct.comp (F.map (hf.lift i h hi)) (hf.fst g) = i

Defined in

Mathlib.CategoryTheory.MorphismProperty.Representable

Cited by

3 results in Mathlib

Foundations

Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.Full