Theorems · Definition · category theory

CochainComplex.mapBifunctor

{C₁ : Type u_1} →
  {C₂ : Type u_2} →
    {D : Type u_3} →
      [inst : CategoryTheory.Category.{v_1, u_1} C₁] →
        [inst_1 : CategoryTheory.Category.{v_2, u_2} C₂] →
          [inst_2 : CategoryTheory.Category.{v_3, u_3} D] →
            [inst_3 : CategoryTheory.Limits.HasZeroMorphisms C₁] →
              [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C₂] →
                (K₁ : CochainComplex C₁ ℤ) →
                  (K₂ : CochainComplex C₂ ℤ) →
                    [inst_5 : CategoryTheory.Preadditive D] →
                      (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ D)) →
                        [inst_6 : F.PreservesZeroMorphisms] →
                          [inst_7 : ∀ (X₁ : C₁), (F.obj X₁).PreservesZeroMorphisms] →
                            [K₁.HasMapBifunctor K₂ F] → CochainComplex D ℤ

Given K₁ : CochainComplex C₁ ℤ, K₂ : CochainComplex C₂ ℤ, a bifunctor F : C₁ ⥤ C₂ ⥤ D, this mapBifunctor K₁ K₂ F : CochainComplex D ℤ is the total complex of the bicomplex obtained by applying F to K₁ and K₂.

Defined in

Mathlib.Algebra.Homology.BifunctorShift

Cited by

14 results in Mathlib

Foundations

Depth 53 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.PreadditiveCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsCochainComplex.HasMapBifunctor