Theorems · Definition · category theory

CategoryTheory.MorphismProperty.Comma.mapLeft

{A : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} A] →
    {B : Type u_2} →
      [inst_1 : CategoryTheory.Category.{v_2, u_2} B] →
        {T : Type u_3} →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} T] →
            (R : CategoryTheory.Functor B T) →
              {P : CategoryTheory.MorphismProperty T} →
                {Q : CategoryTheory.MorphismProperty A} →
                  {W : CategoryTheory.MorphismProperty B} →
                    [inst_3 : Q.IsMultiplicative] →
                      [inst_4 : W.IsMultiplicative] →
                        {L₁ L₂ : CategoryTheory.Functor A T} →
                          (l : L₁ ⟶ L₂) →
                            (∀ (X : CategoryTheory.MorphismProperty.Comma L₂ R P Q W),
                                P (CategoryTheory.CategoryStruct.comp (l.app X.left) X.hom)) →
                              CategoryTheory.Functor (CategoryTheory.MorphismProperty.Comma L₂ R P Q W)
                                (CategoryTheory.MorphismProperty.Comma L₁ R P Q W)

A natural transformation L₁ ⟶ L₂ induces a functor P.Comma L₂ R Q W ⥤ P.Comma L₁ R Q W.

Defined in

Mathlib.CategoryTheory.MorphismProperty.Comma

Cited by

28 results in Mathlib

Foundations

Depth 23 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.MorphismProperty.IsMultiplicativeCategoryTheory.MorphismProperty.IsMultiplicative