Theorems · Definition · category theory

CategoryTheory.Adjunction.leftAdjointCompNatTrans

{C₀ : Type u_1} →
  {C₁ : Type u_2} →
    {C₂ : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C₀] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} C₁] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} C₂] →
            {F₀₁ : CategoryTheory.Functor C₀ C₁} →
              {F₁₂ : CategoryTheory.Functor C₁ C₂} →
                {F₀₂ : CategoryTheory.Functor C₀ C₂} →
                  {G₁₀ : CategoryTheory.Functor C₁ C₀} →
                    {G₂₁ : CategoryTheory.Functor C₂ C₁} →
                      {G₂₀ : CategoryTheory.Functor C₂ C₀} →
                        (F₀₁ ⊣ G₁₀) → (F₁₂ ⊣ G₂₁) → (F₀₂ ⊣ G₂₀) → (G₂₀ ⟶ G₂₁.comp G₁₀) → (F₀₁.comp F₁₂ ⟶ F₀₂)

A natural transformation G₂₀ ⟶ G₂₁ ⋙ G₁₀ involving right adjoint functors induces a natural transformation F₀₁ ⋙ F₁₂ ⟶ F₀₂ between the corresponding left adjoint functors.

Defined in

Mathlib.CategoryTheory.Adjunction.CompositionIso

Cited by

5 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category