Theorems · Definition · category theory

CategoryTheory.NatIso.mapHomologicalComplex

{ι : Type u_1} →
  {W₁ : Type u_3} →
    {W₂ : Type u_4} →
      [inst : CategoryTheory.Category.{v_2, u_3} W₁] →
        [inst_1 : CategoryTheory.Category.{v_3, u_4} W₂] →
          [inst_2 : CategoryTheory.Limits.HasZeroMorphisms W₁] →
            [inst_3 : CategoryTheory.Limits.HasZeroMorphisms W₂] →
              {F G : CategoryTheory.Functor W₁ W₂} →
                [inst_4 : F.PreservesZeroMorphisms] →
                  [inst_5 : G.PreservesZeroMorphisms] →
                    (F ≅ G) → (c : ComplexShape ι) → F.mapHomologicalComplex c ≅ G.mapHomologicalComplex c

A natural isomorphism between functors induces a natural isomorphism between those functors applied to homological complexes.

Defined in

Mathlib.Algebra.Homology.Additive

Cited by

4 results in Mathlib

Foundations

Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphisms