Theorems · Definition · algebraic topology

SSet.chainComplexXCofan

{C : Type u} →
  [inst : CategoryTheory.Category.{v, u} C] →
    [CategoryTheory.Limits.HasCoproducts C] →
      [CategoryTheory.Preadditive C] → (X : SSet) → (R : C) → (n : ℕ) → CategoryTheory.Limits.Cofan fun x => R

The colimit cofan which defines the simplicial n-chains (X.chainComplex R).X n.

Defined in: Mathlib.AlgebraicTopology.SimplicialSet.Homology.Basic
Cited by: 0 results in Mathlib
Foundations: Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CategoryTheory.Category CategoryTheory.Limits.HasCoproducts CategoryTheory.Preadditive

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Cites12

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

CategoryTheory.Categorystatement and proof · cited by 32,673
CategoryTheory.Functor.objstatement · cited by 19,642
Oppositestatement · cited by 8,081
CategoryTheory.Preadditivestatement and proof · cited by 3,309
SimplexCategorystatement · cited by 2,204
HomologicalComplex.Xproof · cited by 1,839
SSetstatement and proof · cited by 1,283
CategoryTheory.Limits.Cofanstatement · cited by 124
CategoryTheory.Limits.HasCoproductsstatement and proof · cited by 119
CategoryTheory.Limits.Cofan.mkproof · cited by 105
SSet.chainComplexproof · cited by 46
SSet.ιChainComplexproof · cited by 20

Cited by1

Results whose statement or proof uses this declaration.

SSet.isColimitChainComplexXCofanstatement · cited by 1