Theorems · Definition · category theory

CategoryTheory.Join.mapIsoWhiskerLeft

{C : Type u₁} →
  [inst : CategoryTheory.Category.{v₁, u₁} C] →
    {D : Type u₂} →
      [inst_1 : CategoryTheory.Category.{v₂, u₂} D] →
        {E : Type u₃} →
          [inst_2 : CategoryTheory.Category.{v₃, u₃} E] →
            {E' : Type u₄} →
              [inst_3 : CategoryTheory.Category.{v₄, u₄} E'] →
                (H : CategoryTheory.Functor C E) →
                  {Fᵣ Gᵣ : CategoryTheory.Functor D E'} →
                    (Fᵣ ≅ Gᵣ) → (CategoryTheory.Join.mapPair H Fᵣ ≅ CategoryTheory.Join.mapPair H Gᵣ)

A natural isomorphism Fᵣ ≅ Gᵣ induces a natural isomorphism mapPair H Fᵣ ≅ mapPair H Gᵣ for every H : C ⥤ E.

Defined in

Mathlib.CategoryTheory.Join.Basic

Cited by

11 results in Mathlib

Foundations

Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Category