Theorems · Definition · category theory

CategoryTheory.Functor.mapBifunctorHomologicalComplex

{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] →
                [inst_5 : CategoryTheory.Limits.HasZeroMorphisms D] →
                  (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ D)) →
                    {I₁ : Type u_4} →
                      {I₂ : Type u_5} →
                        (c₁ : ComplexShape I₁) →
                          (c₂ : ComplexShape I₂) →
                            [F.PreservesZeroMorphisms] →
                              [∀ (X₁ : C₁), (F.obj X₁).PreservesZeroMorphisms] →
                                CategoryTheory.Functor (HomologicalComplex C₁ c₁)
                                  (CategoryTheory.Functor (HomologicalComplex C₂ c₂) (HomologicalComplex₂ D c₁ c₂))

Given a functor F : C₁ ⥤ C₂ ⥤ D, this is the bifunctor which sends K₁ : HomologicalComplex C₁ c₁ and K₂ : HomologicalComplex C₂ c₂ to the bicomplex which is degree (i₁, i₂) consists of (F.obj (K₁.X i₁)).obj (K₂.X i₂).

Defined in

Mathlib.Algebra.Homology.Bifunctor

Cited by

35 results in Mathlib

Foundations

Depth 31 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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