Theorems · Theorem · algebraic topology

SSet.normalizedChainComplex_hom_ext_iff

∀ {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} {T : C}
  {f g : (X.normalizedChainComplex R).X n ⟶ T},
  f = g ↔
    ∀ x ∈ X.nonDegenerate n,
      CategoryTheory.CategoryStruct.comp (X.ιNormalizedChainComplex x) f =
        CategoryTheory.CategoryStruct.comp (X.ιNormalizedChainComplex x) g

Defined in

Mathlib.AlgebraicTopology.SimplicialSet.Homology.Nondegenerate

Cited by

0 results in Mathlib

Foundations

Depth 108 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.Preadditive