Theorems · Definition · category theory

CategoryTheory.Functor.relativelyRepresentable.symmetry

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {F : CategoryTheory.Functor C D} →
          {Y : D} →
            {b : C} →
              {f' : F.obj b ⟶ Y} →
                (hf' : F.relativelyRepresentable f') →
                  {a : C} →
                    {g : F.obj a ⟶ Y} → (hg : F.relativelyRepresentable g) → [F.Full] → hf'.pullback g ⟶ hg.pullback f'

Given two representable morphisms f' : F.obj b ⟶ Y and g : F.obj a ⟶ Y, we obtain an isomorphism hf'.pullback g ⟶ hg.pullback f'.

Defined in

Mathlib.CategoryTheory.MorphismProperty.Representable

Cited by

10 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Functor.Full