Theorems · Definition · category theory

CategoryTheory.NatTrans.mapHomotopyCategory

{ι : Type u_2} →
  {V : Type u} →
    [inst : CategoryTheory.Category.{v, u} V] →
      [inst_1 : CategoryTheory.Preadditive V] →
        {W : Type u_3} →
          [inst_2 : CategoryTheory.Category.{v_1, u_3} W] →
            [inst_3 : CategoryTheory.Preadditive W] →
              {F G : CategoryTheory.Functor V W} →
                [inst_4 : F.Additive] →
                  [inst_5 : G.Additive] →
                    (F ⟶ G) → (c : ComplexShape ι) → F.mapHomotopyCategory c ⟶ G.mapHomotopyCategory c

A natural transformation induces a natural transformation between the induced functors on the homotopy category.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory

Cited by

3 results in Mathlib

Foundations

Depth 30 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.Functor.AdditiveCategoryTheory.Functor.Additive