Theorems · Theorem · category theory

CategoryTheory.ShortComplex.HomologyMapData.ofIsLimitKernelFork_left

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Limits.HasZeroMorphisms C]
  {S₁ S₂ : CategoryTheory.ShortComplex C} (φ : S₁ ⟶ S₂) (hf₁ : S₁.f = 0) (c₁ : CategoryTheory.Limits.KernelFork S₁.g)
  (hc₁ : CategoryTheory.Limits.IsLimit c₁) (hf₂ : S₂.f = 0) (c₂ : CategoryTheory.Limits.KernelFork S₂.g)
  (hc₂ : CategoryTheory.Limits.IsLimit c₂) (f : c₁.pt ⟶ c₂.pt)
  (comm :
    CategoryTheory.CategoryStruct.comp (CategoryTheory.Limits.Fork.ι c₁) φ.τ₂ =
      CategoryTheory.CategoryStruct.comp f (CategoryTheory.Limits.Fork.ι c₂)),
  (CategoryTheory.ShortComplex.HomologyMapData.ofIsLimitKernelFork φ hf₁ c₁ hc₁ hf₂ c₂ hc₂ f comm).left =
    CategoryTheory.ShortComplex.LeftHomologyMapData.ofIsLimitKernelFork φ hf₁ c₁ hc₁ hf₂ c₂ hc₂ f comm

Defined in

Mathlib.Algebra.Homology.ShortComplex.Homology

Cited by

0 results in Mathlib

Foundations

Depth 39 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasZeroMorphisms