Theorems · Definition · category theory

HomologicalComplex.HasMapBifunctor

{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] →
            {I₁ : Type u_4} →
              {I₂ : Type u_5} →
                {J : Type u_6} →
                  {c₁ : ComplexShape I₁} →
                    {c₂ : ComplexShape I₂} →
                      [inst_3 : CategoryTheory.Limits.HasZeroMorphisms C₁] →
                        [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C₂] →
                          [inst_5 : CategoryTheory.Preadditive D] →
                            HomologicalComplex C₁ c₁ →
                              HomologicalComplex C₂ c₂ →
                                (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ D)) →
                                  [F.PreservesZeroMorphisms] →
                                    [∀ (X₁ : C₁), (F.obj X₁).PreservesZeroMorphisms] →
                                      (c : ComplexShape J) → [TotalComplexShape c₁ c₂ c] → Prop

The condition that ((F.mapBifunctorHomologicalComplex c₁ c₂).obj K₁).obj K₂ has a total complex.

Defined in

Mathlib.Algebra.Homology.Bifunctor

Cited by

103 results in Mathlib

Foundations

Depth 32 from the axioms, rests on 275 definitions · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.PreadditiveCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsTotalComplexShape