Theorems · Definition · algebraic topology

SSet.isColimitChainComplexXCofan

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasCoproducts C] →
      [inst_2 : CategoryTheory.Preadditive C] →
        (X : SSet) → (R : C) → (n : ℕ) → CategoryTheory.Limits.IsColimit (X.chainComplexXCofan R n)

Simplicial n-chains (X.chainComplex R).X n of a simplicial set X with coefficients in R identify to a coproduct of copies of R indexed by X _⦋n⦌.

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Homology.Basic

Cited by

1 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.Preadditive