Theorems · Definition · category theory

CochainComplex.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] →
            [inst_3 : CategoryTheory.Limits.HasZeroMorphisms C₁] →
              [inst_4 : CategoryTheory.Limits.HasZeroMorphisms C₂] →
                CochainComplex C₁ ℤ →
                  CochainComplex C₂ ℤ →
                    [inst_5 : CategoryTheory.Preadditive D] →
                      (F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ D)) →
                        [F.PreservesZeroMorphisms] → [∀ (X₁ : C₁), (F.obj X₁).PreservesZeroMorphisms] → Prop

The condition that ((F.mapBifunctorHomologicalComplex _ _).obj K₁).obj K₂ has a total cochain complex.

Defined in

Mathlib.Algebra.Homology.BifunctorShift

Cited by

15 results in Mathlib

Foundations

Depth 52 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

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