Theorems · Theorem · category theory

CochainComplex.HasMapBifunctor.congr_simp

∀ {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 K₁_1 : CochainComplex C₁ ℤ),
  K₁ = K₁_1 →
    ∀ (K₂ K₂_1 : CochainComplex C₂ ℤ),
      K₂ = K₂_1 →
        ∀ [inst_5 : CategoryTheory.Preadditive D] (F F_1 : CategoryTheory.Functor C₁ (CategoryTheory.Functor C₂ D))
          (e_F : F = F_1) [inst_6 : F.PreservesZeroMorphisms] [inst_7 : ∀ (X₁ : C₁), (F.obj X₁).PreservesZeroMorphisms],
          K₁.HasMapBifunctor K₂ F = K₁_1.HasMapBifunctor K₂_1 F_1

Defined in

Mathlib.Algebra.Homology.BifunctorShift

Cited by

0 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.PreservesZeroMorphisms