Theorems · Definition · category theory

CochainComplex.HomComplex.Cocycle.mk

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {F G : CochainComplex C ℤ} →
        {n : ℤ} →
          (z : CochainComplex.HomComplex.Cochain F G n) →
            (m : ℤ) → n + 1 = m → CochainComplex.HomComplex.δ n m z = 0 → CochainComplex.HomComplex.Cocycle F G n

Constructor for Cocycle F G n, taking as inputs z : Cochain F G n, an integer m : ℤ such that n + 1 = m, and the relation δ n m z = 0.

Defined in

Mathlib.Algebra.Homology.HomotopyCategory.HomComplex

Cited by

6 results in Mathlib

Foundations

Depth 56 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Preadditive