Theorems · Theorem · algebraic topology
AlgebraicTopology.DoldKan.P_f_0_eq
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
{X : CategoryTheory.SimplicialObject C} (q : ℕ),
(AlgebraicTopology.DoldKan.P q).f 0 =
CategoryTheory.CategoryStruct.id ((AlgebraicTopology.AlternatingFaceMapComplex.obj X).X 0)All the P q coincide with 𝟙 _ in degree 0.
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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.compproof · cited by 17,999
- CategoryTheory.CategoryStruct.idstatement and proof · cited by 6,235
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- add_zeroproof · cited by 2,707
- CategoryTheory.Category.id_compproof · cited by 1,998
- HomologicalComplex.Xstatement and proof · 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 and proof · cited by 146
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.P_f_idemproof · cited by 5
- AlgebraicTopology.DoldKan.PInfty_on_Γ₀_splitting_summand_eq_selfproof · cited by 2
- AlgebraicTopology.DoldKan.P_is_eventually_constantproof · cited by 1
- AlgebraicTopology.DoldKan.Q_f_0_eqproof · cited by 0