Theorems · Definition · algebraic topology
AlgebraicTopology.DoldKan.PInfty
{C : Type u_1} →
[inst : CategoryTheory.Category.{v_1, u_1} C] →
[inst_1 : CategoryTheory.Preadditive C] →
{X : CategoryTheory.SimplicialObject C} →
AlgebraicTopology.AlternatingFaceMapComplex.obj X ⟶ AlgebraicTopology.AlternatingFaceMapComplex.obj XThe endomorphism PInfty : K[X] ⟶ K[X] obtained from the P q by passing to the limit.
- Defined in
- Mathlib.AlgebraicTopology.DoldKan.PInfty
- Cited by
- 94 results in Mathlib
- Foundations
- Depth 86 from the axioms, rests on 2,468 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites10
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
- Quiver.Homstatement · cited by 32,603
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplex.Hom.fproof · cited by 845
- ComplexShape.downstatement · cited by 605
- CategoryTheory.SimplicialObjectstatement and proof · cited by 548
- ChainComplexstatement · cited by 350
- AlgebraicTopology.AlternatingFaceMapComplex.objstatement · cited by 146
- AlgebraicTopology.DoldKan.Pproof · cited by 38
- ChainComplex.ofHomproof · cited by 0
Cited by105
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.N₁proof · cited by 43
- AlgebraicTopology.DoldKan.QInftyproof · cited by 20
- CategoryTheory.SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁proof · cited by 16
- AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplexproof · cited by 10
- CategoryTheory.SimplicialObject.Splitting.toNondegComplexproof · cited by 9
- AlgebraicTopology.DoldKan.PInfty_f_idemstatement · cited by 7
- CategoryTheory.SimplicialObject.Splitting.fromNondegComplexproof · cited by 7
- AlgebraicTopology.DoldKan.PInfty_idemstatement and proof · cited by 5
- AlgebraicTopology.DoldKan.Γ₂N₁.natTransproof · cited by 4
- AlgebraicTopology.DoldKan.PInfty_f_naturalitystatement · cited by 4
- AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInftystatement and proof · cited by 4
- AlgebraicTopology.DoldKan.σ_comp_PInftystatement · cited by 4