Theorems · Definition · category theory
CategoryTheory.Idempotents.DoldKan.equivalence
{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.SimplicialObject C ≌ ChainComplex C ℕThe Dold-Kan equivalence for pseudoabelian categories given
by the functors N and Γ. It is obtained by applying the results in
Compatibility.lean to the equivalence Preadditive.DoldKan.Equivalence.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 118 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- Oppositestatement · cited by 8,081
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- SimplexCategorystatement · cited by 2,204
- ComplexShape.downstatement · cited by 605
- CategoryTheory.Equivalencestatement · cited by 601
- CategoryTheory.SimplicialObjectstatement · cited by 548
- ChainComplexstatement · cited by 350
- CategoryTheory.Limits.HasFiniteCoproductsstatement and proof · cited by 110
- CategoryTheory.IsIdempotentCompletestatement and proof · cited by 29
- AlgebraicTopology.DoldKan.Compatibility.equivalenceproof · cited by 4
- CategoryTheory.Idempotents.DoldKan.isoN₁proof · cited by 3
Cited by5
Results whose statement or proof uses this declaration.
- CategoryTheory.Abelian.DoldKan.equivalenceproof · cited by 2
- CategoryTheory.Idempotents.DoldKan.equivalence_inversestatement · cited by 0
- CategoryTheory.Idempotents.DoldKan.equivalence_unitIsostatement · cited by 0
- CategoryTheory.Idempotents.DoldKan.equivalence_counitIsostatement · cited by 0
- CategoryTheory.Idempotents.DoldKan.equivalence_functorstatement · cited by 0