Theorems · Definition · algebraic topology

AlgebraicTopology.singularChainComplexFunctorAdjunction

(C : Type u) →
  [inst : CategoryTheory.Category.{v, u} C] →
    [inst_1 : CategoryTheory.Limits.HasCoproducts C] →
      [inst_2 : CategoryTheory.Preadditive C] →
        (n : ℕ) →
          (CategoryTheory.Functor.postcompose₂.obj (HomologicalComplex.eval C (ComplexShape.down ℕ) n)).obj
              (AlgebraicTopology.singularChainComplexFunctor C) ⊣
            (CategoryTheory.evaluation TopCat C).obj (SimplexCategory.toTop.{w}.obj { len := n })

The adjunction Hom(Cⁿ(-, X), F) ≃ Hom(X, F(Δ[n])) for X : C and F : Top ⥤ C.

Defined in

Mathlib.AlgebraicTopology.SingularHomology.Basic

Cited by

2 results in Mathlib

Foundations

Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.Limits.HasCoproductsCategoryTheory.Preadditive