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Theorems · Definition · algebraic topology

AlgebraicTopology.DoldKan.Q

{C : Type u_1} →
  [inst : CategoryTheory.Category.{v_1, u_1} C] →
    [inst_1 : CategoryTheory.Preadditive C] →
      {X : CategoryTheory.SimplicialObject C} →
        ℕ → (AlgebraicTopology.AlternatingFaceMapComplex.obj X ⟶ AlgebraicTopology.AlternatingFaceMapComplex.obj X)

Q q is the complement projection associated to P q

Defined in
Mathlib.AlgebraicTopology.DoldKan.Projections
Cited by
18 results in Mathlib
Foundations
Depth 77 from the axioms · 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.decomposition_Q · cited by 4DoldKan.decomposition_QAlgebraicTopology.DoldKan.P_add_Q_f · cited by 3DoldKan.P_add_Q_fAlgebraicTopology.DoldKan.Q_f_idem · cited by 3DoldKan.Q_f_idemAlgebraicTopology.DoldKan.Q_f_naturality · cited by 2DoldKan.Q_f_naturalityAlgebraicTopology.DoldKan.Q_idem · cited by 1DoldKan.Q_idemAlgebraicTopology.DoldKan.Q_is_eventually_constant · cited by 1DoldKan.Q_is_eventually_c…AlgebraicTopology.DoldKan.Q_succ · cited by 1DoldKan.Q_succAlgebraicTopology.DoldKan.Q_zero · cited by 1DoldKan.Q_zeroAlgebraicTopology.DoldKan.σ_comp_P_eq_zero · cited by 1DoldKan.σ_comp_P_eq_zeroAlgebraicTopology.DoldKan.P_add_Q · cited by 1DoldKan.P_add_QAlgebraicTopology.DoldKan.QInfty_f · cited by 1DoldKan.QInfty_fAlgebraicTopology.DoldKan.natTransQ · cited by 1DoldKan.natTransQAlgebraicTopology.DoldKan.Q_f_naturality_assoc · cited by 0DoldKan.Q_f_naturality_as…AlgebraicTopology.DoldKan.Q_idem_assoc · cited by 0DoldKan.Q_idem_assocAlgebraicTopology.DoldKan.Q_f_0_eq · cited by 0DoldKan.Q_f_0_eqCategoryTheory.Category · cited by 32673CategoryTheory.CategoryQuiver.Hom · cited by 32603Quiver.HomCategoryTheory.CategoryStruct.id · cited by 6235CategoryStruct.idCategoryTheory.Preadditive · cited by 3309CategoryTheory.PreadditiveComplexShape.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.PDoldKan.QCITED BYCITES

Cites9

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Cited by20

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