Theorems · Definition · category theory

CategoryTheory.Idempotents.DoldKan.N

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      [CategoryTheory.IsIdempotentComplete C] →
        [CategoryTheory.Limits.HasFiniteCoproducts C] →
          CategoryTheory.Functor (CategoryTheory.SimplicialObject C) (ChainComplex C ℕ)

The functor N for the equivalence is obtained by composing N' : SimplicialObject C ⥤ Karoubi (ChainComplex C ℕ) and the inverse of the equivalence ChainComplex C ℕ ≌ Karoubi (ChainComplex C ℕ).

Defined in

Mathlib.AlgebraicTopology.DoldKan.EquivalencePseudoabelian

Cited by

7 results in Mathlib

Foundations

Depth 93 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CategoryTheory.CategoryCategoryTheory.PreadditiveCategoryTheory.IsIdempotentCompleteCategoryTheory.Limits.HasFiniteCoproducts