Theorems · Theorem · category theory

HomologicalComplex.mapBifunctor.hom_ext

∀ {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] {K₁ : HomologicalComplex C₁ c₁} {K₂ : HomologicalComplex C₂ c₂}
  {F : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ D)} [inst_6 : F.PreservesZeroMorphisms]
  [inst_7 : ∀ (X₁ : C₁), (F.obj X₁).PreservesZeroMorphisms] {c : ComplexShape J} [inst_8 : TotalComplexShape c₁ c₂ c]
  [inst_9 : K₁.HasMapBifunctor K₂ F c] [inst_10 : DecidableEq J] {Y : D} {j : J}
  {f g : (K₁.mapBifunctor K₂ F c).X j ⟶ Y},
  (∀ (i₁ : I₁) (i₂ : I₂) (h : c₁.π c₂ c (i₁, i₂) = j),
      CategoryTheory.CategoryStruct.comp (K₁.ιMapBifunctor K₂ F c i₁ i₂ j h) f =
        CategoryTheory.CategoryStruct.comp (K₁.ιMapBifunctor K₂ F c i₁ i₂ j h) g) →
    f = g

Defined in

Mathlib.Algebra.Homology.Bifunctor

Cited by

6 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.Limits.HasZeroMorphismsCategoryTheory.PreadditiveCategoryTheory.Functor.PreservesZeroMorphismsCategoryTheory.Functor.PreservesZeroMorphismsTotalComplexShapeHomologicalComplex.HasMapBifunctorDecidableEq