Theorems · Theorem · category theory
AlgebraicTopology.AlternatingFaceMapComplex.obj_d_eq
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
(X : CategoryTheory.SimplicialObject C) (n : ℕ),
(AlgebraicTopology.AlternatingFaceMapComplex.obj X).d (n + 1) n = ∑ i, (-1) ^ ↑i • X.δ i- Cited by
- 7 results in Mathlib
- Foundations
- Depth 72 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
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.Functor.objstatement and proof · cited by 19,642
- Oppositestatement · cited by 8,081
- Finset.sumstatement and proof · cited by 5,195
- Finset.univstatement and proof · cited by 3,473
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- SimplexCategorystatement · cited by 2,204
- HomologicalComplex.Xstatement · cited by 1,839
- ComplexShape.downstatement · cited by 605
- HomologicalComplex.dstatement · cited by 598
- CategoryTheory.SimplicialObjectstatement and proof · cited by 548
Cited by7
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eqproof · cited by 4
- AlgebraicTopology.alternatingFaceMapComplex_obj_dproof · cited by 3
- AlgebraicTopology.DoldKan.HigherFacesVanish.comp_Hσ_eq_zeroproof · cited by 3
- AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInftyproof · cited by 1
- AlgebraicTopology.DoldKan.σ_comp_P_eq_zeroproof · cited by 1
- AlgebraicTopology.DoldKan.Hσ_eq_zeroproof · cited by 1
- AlgebraicTopology.karoubi_alternatingFaceMapComplex_dproof · cited by 1