Theorems · Definition · category theory

CategoryTheory.Functor.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 : CategoryTheory.Functor W₁ W₂) →
                [F.PreservesZeroMorphisms] →
                  (c : ComplexShape ι) → CategoryTheory.Functor (HomologicalComplex W₁ c) (HomologicalComplex W₂ c)

An additive functor induces a functor between homological complexes. This is sometimes called the "prolongation".

Defined in

Mathlib.Algebra.Homology.Additive

Cited by

145 results in Mathlib

Foundations

Depth 20 from the axioms, rests on 111 definitions · uses propext, Classical.choice, Quot.sound

Assumes

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