Theorems · Theorem · category theory

CochainComplex.HomComplex.Cochain.comp_v

∀ {C : Type u} [inst : CategoryTheory.Category.{v, u} C] [inst_1 : CategoryTheory.Preadditive C]
  {F G K : CochainComplex C ℤ} {n₁ n₂ n₁₂ : ℤ} (z₁ : CochainComplex.HomComplex.Cochain F G n₁)
  (z₂ : CochainComplex.HomComplex.Cochain G K n₂) (h : n₁ + n₂ = n₁₂) (p₁ p₂ p₃ : ℤ) (h₁ : p₁ + n₁ = p₂)
  (h₂ : p₂ + n₂ = p₃), (z₁.comp z₂ h).v p₁ p₃ ⋯ = CategoryTheory.CategoryStruct.comp (z₁.v p₁ p₂ h₁) (z₂.v p₂ p₃ h₂)

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplex

Cited by

30 results in Mathlib

Foundations

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

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive