Theorems · Theorem · algebraic topology
AlgebraicTopology.DoldKan.PInfty_comp_map_mono_eq_zero
∀ {C : Type u_1} [inst : CategoryTheory.Category.{v_1, u_1} C] [inst_1 : CategoryTheory.Preadditive C]
(X : CategoryTheory.SimplicialObject C) {n : ℕ} {Δ' : SimplexCategory} (i : Δ' ⟶ { len := n })
[hi : CategoryTheory.Mono i],
Δ'.len ≠ n →
¬AlgebraicTopology.DoldKan.Isδ₀ i →
CategoryTheory.CategoryStruct.comp (AlgebraicTopology.DoldKan.PInfty.f n) (X.map i.op) = 0- Cited by
- 1 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.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CategoryTheory.Categorystatement and proof · cited by 32,673
- Quiver.Homstatement and proof · cited by 32,603
- CategoryTheory.Functor.objstatement and proof · cited by 19,642
- CategoryTheory.CategoryStruct.compstatement and proof · cited by 17,999
- CategoryTheory.Functor.mapstatement and proof · cited by 8,698
- Oppositestatement and proof · cited by 8,081
- CategoryTheory.Category.assocproof · cited by 6,433
- CategoryTheory.Preadditivestatement and proof · cited by 3,309
- SimplexCategorystatement and proof · cited by 2,204
- Quiver.Hom.opstatement and proof · cited by 1,948
- HomologicalComplex.Xstatement and proof · cited by 1,839
Cited by1
Results whose statement or proof uses this declaration.
- AlgebraicTopology.DoldKan.Γ₀_obj_termwise_mapMono_comp_PInftyproof · cited by 1