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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 X

The 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
Assumes
CategoryTheory.CategoryCategoryTheory.Preadditive

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicTopology.DoldKan.N₁ · cited by 43DoldKan.N₁AlgebraicTopology.DoldKan.QInfty · cited by 20DoldKan.QInftyCategoryTheory.SimplicialObject.Splitting.toKaroubiNondegComplexIsoN₁ · cited by 16Splitting.toKaroubiNondeg…AlgebraicTopology.DoldKan.PInftyToNormalizedMooreComplex · cited by 10DoldKan.PInftyToNormalize…CategoryTheory.SimplicialObject.Splitting.toNondegComplex · cited by 9Splitting.toNondegComplexAlgebraicTopology.DoldKan.PInfty_f_idem · cited by 7DoldKan.PInfty_f_idemCategoryTheory.SimplicialObject.Splitting.fromNondegComplex · cited by 7Splitting.fromNondegCompl…AlgebraicTopology.DoldKan.PInfty_idem · cited by 5DoldKan.PInfty_idemAlgebraicTopology.DoldKan.Γ₂N₁.natTrans · cited by 4Γ₂N₁.natTransAlgebraicTopology.DoldKan.PInfty_f_naturality · cited by 4DoldKan.PInfty_f_naturali…AlgebraicTopology.DoldKan.factors_normalizedMooreComplex_PInfty · cited by 4DoldKan.factors_normalize…AlgebraicTopology.DoldKan.σ_comp_PInfty · cited by 4DoldKan.σ_comp_PInftyAlgebraicTopology.DoldKan.MorphComponents.id · cited by 3MorphComponents.idAlgebraicTopology.DoldKan.MorphComponents.φ · cited by 3MorphComponents.φAlgebraicTopology.DoldKan.PInfty_f · cited by 3DoldKan.PInfty_fCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveHomologicalComplex.Hom.f · cited by 845Hom.fComplexShape.down · cited by 605ComplexShape.downCategoryTheory.SimplicialObject · cited by 548CategoryTheory.Simplicial…ChainComplex · cited by 350ChainComplexAlgebraicTopology.AlternatingFaceMapComplex.obj · cited by 146AlternatingFaceMapComplex…AlgebraicTopology.DoldKan.P · cited by 38DoldKan.PChainComplex.ofHom · cited by 0ChainComplex.ofHomDoldKan.PInftyCITED BYCITES

Cites10

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Cited by105

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