Theorems · Theorem · algebraic topology
AlgebraicTopology.DoldKan.PInfty_f_idem
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
{X : CategoryTheory.SimplicialObject C} (n : ℕ),
CategoryTheory.CategoryStruct.comp (AlgebraicTopology.DoldKan.PInfty.f n) (AlgebraicTopology.DoldKan.PInfty.f n) =
AlgebraicTopology.DoldKan.PInfty.f n- Defined in
- Mathlib.AlgebraicTopology.DoldKan.PInfty
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.CategoryStruct.compstatement · cited by 17,999
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- HomologicalComplex.Xstatement · cited by 1,839
- HomologicalComplex.Hom.fstatement and proof · cited by 845
- ComplexShape.downstatement · cited by 605
- CategoryTheory.SimplicialObjectstatement and proof · cited by 548
- AlgebraicTopology.AlternatingFaceMapComplex.objstatement · cited by 146
- AlgebraicTopology.DoldKan.PInftystatement · cited by 94
- AlgebraicTopology.DoldKan.Pproof · cited by 38
- AlgebraicTopology.DoldKan.P_f_idemproof · cited by 5
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.PInfty_idemproof · cited by 5
- AlgebraicTopology.DoldKan.PInfty_f_idem_assocproof · cited by 3
- CategoryTheory.SimplicialObject.Splitting.PInfty_comp_πSummand_idproof · cited by 2
- AlgebraicTopology.DoldKan.QInfty_f_comp_PInfty_fproof · cited by 2
- AlgebraicTopology.DoldKan.PInfty_f_comp_QInfty_fproof · cited by 2
- AlgebraicTopology.DoldKan.PInfty_comp_PInftyToNormalizedMooreComplexproof · cited by 1
- AlgebraicTopology.DoldKan.N₂Γ₂ToKaroubiIso_hom_appproof · cited by 1