Theorems · Definition · category theory

CategoryTheory.Functor.Final.homToLift

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        (F : CategoryTheory.Functor C D) →
          [inst_2 : F.Final] → (d : D) → d ⟶ F.obj (CategoryTheory.Functor.Final.lift F d)

When F : C ⥤ D is final, we denote by homToLift an arbitrary choice of morphism d ⟶ F.obj (lift F d).

Defined in

Mathlib.CategoryTheory.Limits.Final

Cited by

4 results in Mathlib

Foundations

Depth 29 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.Final